DF-space

<h2 id="definition">Definition</h2>
A <a href="/facts/Locally_convex_topological_vector_space/AGrPrayC">locally convex topological vector space</a> (TVS) 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a DF-space, also written (DF)-space, if<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a>

<ol><li>
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a <a href="/facts/Countably_quasi-barrelled_space/q1SuqeYk">countably quasi-barrelled space</a> (i.e. every strongly bounded countable union of equicontinuous subsets of 
 
 
 
 
 X
 
 ′
 
 
 
 
 {\displaystyle X^{\prime }}
 
 is equicontinuous), and</li>
<li>
 
 
 
 X
 
 
 {\displaystyle X}
 
 possesses a fundamental sequence of bounded (i.e. there exists a countable sequence of bounded subsets 
 
 
 
 
 B
 
 1
 
 
 ,
 
 B
 
 2
 
 
 ,
 …
 
 
 {\displaystyle B_{1},B_{2},\ldots }
 
 such that every bounded subset of 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is contained in some 
 
 
 
 
 B
 
 i
 
 
 
 
 {\displaystyle B_{i}}
 
<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a>).</li></ol>
<h2 id="properties">Properties</h2>
<ul>
<li>Let 
 
 
 
 X
 
 
 {\displaystyle X}
 
 be a DF-space and let 
 
 
 
 V
 
 
 {\displaystyle V}
 
 be a convex balanced subset of 
 
 
 
 X
 .
 
 
 {\displaystyle X.}
 
 Then 
 
 
 
 V
 
 
 {\displaystyle V}
 
 is a neighborhood of the origin if and only if for every convex, balanced, bounded subset 
 
 
 
 B
 ⊆
 X
 ,
 
 
 {\displaystyle B\subseteq X,}
 
 
 
 
 
 B
 ∩
 V
 
 
 {\displaystyle B\cap V}
 
 is a neighborhood of the origin in 
 
 
 
 B
 .
 
 
 {\displaystyle B.}
 
<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> Consequently, a linear map from a DF-space into a locally convex space is continuous if its restriction to each bounded subset of the domain is continuous.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a></li>
<li>The <a href="/facts/Strong_dual_space/4RI1SYl6">strong dual space</a> of a DF-space is a <a href="/facts/Fr%25C3%25A9chet_space/9gXkQu2u">Fréchet space</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a></li>
<li>Every infinite-dimensional <a href="/facts/Montel_space/HLXqXHzs">Montel</a> DF-space is a <a href="/facts/Sequential_space/xAjFpdfR">sequential space</a> but not a <a href="/facts/Fr%25C3%25A9chet%25E2%2580%2593Urysohn_space/ccN00rSh">Fréchet–Urysohn space</a>.</li>
<li>Suppose 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is either a DF-space or an <a href="/facts/LM-space/6FUHfx6W">LM-space</a>. If 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a <a href="/facts/Sequential_space/xAjFpdfR">sequential space</a> then it is either <a href="/facts/Metrizable_topological_vector_space/6FUHfx6W">metrizable</a> or else a <a href="/facts/Montel_space/HLXqXHzs">Montel space</a> DF-space.</li>
<li>Every <a href="/facts/Quasi-complete/rQPDf5nu">quasi-complete</a> DF-space is complete.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a></li>
<li>If 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a <a href="/facts/Complete_topological_vector_space/e6qtS76j">complete</a> <a href="/facts/Nuclear_space/4FLPWdfp">nuclear</a> DF-space then 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a <a href="/facts/Montel_space/HLXqXHzs">Montel space</a>.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a></li>
</ul>
<h2 id="sufficient-conditions">Sufficient conditions</h2>
The <a href="/facts/Strong_dual_space/4RI1SYl6">strong dual space</a> 
 
 
 
 
 X
 
 b
 
 
 ′
 
 
 
 
 {\displaystyle X_{b}^{\prime }}
 
 of a Fréchet space 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a DF-space.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a>

<ul>
<li>The strong dual of a metrizable locally convex space is a DF-space<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> but the convers is in general not true<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> (the converse being the statement that every DF-space is the strong dual of some metrizable locally convex space). From this it follows: 
<ul><li>Every normed space is a DF-space.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a></li>
<li>Every Banach space is a DF-space.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a></li>
<li>Every <a href="/facts/Infrabarreled_space/SaoLAH83">infrabarreled space</a> possessing a fundamental sequence of bounded sets is a DF-space.</li></ul>
</li><li>Every Hausdorff quotient of a DF-space is a DF-space.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a></li>
<li>The <a href="/facts/Complete_topological_vector_space/e6qtS76j">completion</a> of a DF-space is a DF-space.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a></li>
<li>The locally convex sum of a sequence of DF-spaces is a DF-space.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a></li>
<li>An inductive limit of a sequence of DF-spaces is a DF-space.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a></li>
<li>Suppose that 
 
 
 
 X
 
 
 {\displaystyle X}
 
 and 
 
 
 
 Y
 
 
 {\displaystyle Y}
 
 are DF-spaces. Then the <a href="/facts/Projective_tensor_product/lv5X7Ps7">projective tensor product</a>, as well as its completion, of these spaces is a DF-space.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a></li><li>
</li></ul>
However,

<ul>
<li>An infinite product of non-trivial DF-spaces (i.e. all factors have non-0 dimension) is not a DF-space.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a></li>
<li>A closed vector subspace of a DF-space is not necessarily a DF-space.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a></li>
<li>There exist complete DF-spaces that are not TVS-isomorphic to the strong dual of a metrizable locally convex TVS.<a class="footnote-ref" id="fnref:22" href="#fn:22">22</a></li>
</ul>
<h2 id="examples">Examples</h2>
There exist complete DF-spaces that are not TVS-isomorphic with the strong dual of a metrizable locally convex space.<a class="footnote-ref" id="fnref:23" href="#fn:23">23</a>
There exist DF-spaces having closed vector subspaces that are not DF-spaces.<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Barreled_space/r2H58TN3">Barreled space</a> – Type of topological vector spacePages displaying short descriptions of redirect targets</li>
<li><a href="/facts/Countably_quasi-barrelled_space/q1SuqeYk">Countably quasi-barrelled space</a></li>
<li><a href="/facts/F-space/NBCcYfcU">F-space</a> – Topological vector space with a complete translation-invariant metric</li>
<li><a href="/facts/LB-space/Dg19Fq32">LB-space</a></li>
<li><a href="/facts/LF-space/voQHEeGI">LF-space</a> – Topological vector space</li>
<li><a href="/facts/Nuclear_space/4FLPWdfp">Nuclear space</a> – A generalization of finite-dimensional Euclidean spaces different from Hilbert spaces</li>
<li><a href="/facts/Projective_tensor_product/lv5X7Ps7">Projective tensor product</a> – tensor product defined on two topological vector spacesPages displaying wikidata descriptions as a fallback</li></ul>
<h2 id="citations">Citations</h2>

<h2 id="bibliography">Bibliography</h2>
<ul><li><a href="/facts/Alexander_Grothendieck/jLQGPY7M">Grothendieck, Alexander</a> (1954). "Sur les espaces (F) et (DF)". Summa Brasil. Math. (in French). 3: 57–123. <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0075542">0075542</a>.</li>
<li><a href="/facts/Alexander_Grothendieck/jLQGPY7M">Grothendieck, Alexander</a> (1955). "Produits Tensoriels Topologiques et Espaces Nucléaires" [Topological Tensor Products and Nuclear Spaces]. Memoirs of the American Mathematical Society Series (in French). 16. Providence: American Mathematical Society. <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0075539">0075539</a>. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/9308061">9308061</a>.</li>
<li>Khaleelulla, S. M. (1982). Counterexamples in Topological Vector Spaces. <a href="/facts/Lecture_Notes_in_Mathematics/5DmSFMhJ">Lecture Notes in Mathematics</a>. Vol. 936. Berlin, Heidelberg, New York: <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-11565-6. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/8588370">8588370</a>.</li>
<li>Pietsch, Albrecht (1979). Nuclear Locally Convex Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete. Vol. 66 (Second ed.). Berlin, New York: Springer-Verlag. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-05644-9. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/539541">539541</a>.</li>
<li>Pietsch, Albrecht (1972). Nuclear locally convex spaces. Berlin, New York: Springer-Verlag. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-05644-0. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/539541">539541</a>.</li>
<li><a href="/facts/Helmut_H._Schaefer/xorHTDBE">Schaefer, Helmut H.</a>; Wolff, Manfred P. (1999). Topological Vector Spaces. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">GTM</a>. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4612-7155-0. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/840278135">840278135</a>.</li>
<li>Wong, Yau-Chuen (1979). Schwartz Spaces, Nuclear Spaces, and Tensor Products. <a href="/facts/Lecture_Notes_in_Mathematics/5DmSFMhJ">Lecture Notes in Mathematics</a>. Vol. 726. Berlin New York: <a href="/facts/Springer_Publishing/JfRev59b">Springer-Verlag</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-09513-2. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/5126158">5126158</a>.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="https://ncatlab.org/nlab/show/DF+space">DF-space at ncatlab</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Schaefer & Wolff 1999, pp. 154–155. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Schaefer & Wolff 1999, pp. 152, 154. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Schaefer & Wolff 1999, pp. 154–155. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Schaefer & Wolff 1999, p. 25. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Schaefer & Wolff 1999, pp. 154–155. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Schaefer & Wolff 1999, pp. 154–155. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Schaefer & Wolff 1999, p. 196. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Schaefer & Wolff 1999, pp. 190–202. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Schaefer & Wolff 1999, pp. 199–202. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Gabriyelyan, S.S. "On topological spaces and topological groups with certain local countable networks (2014) <a href="https://arxiv.org/pdf/1412.1497.pdf" target="_blank">https://arxiv.org/pdf/1412.1497.pdf</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Schaefer & Wolff 1999, p. 154. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Schaefer & Wolff 1999, p. 154. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Khaleelulla 1982, p. 33. - Khaleelulla, S. M. (1982). Counterexamples in Topological Vector Spaces. Lecture Notes in Mathematics. Vol. 936. Berlin, Heidelberg, New York: Springer-Verlag. ISBN 978-3-540-11565-6. OCLC 8588370. <a href="https://search.worldcat.org/oclc/8588370" target="_blank">https://search.worldcat.org/oclc/8588370</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Schaefer & Wolff 1999, pp. 154–155. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">Schaefer & Wolff 1999, pp. 199–202. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">Schaefer & Wolff 1999, pp. 196–197. - Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. <a href="https://search.worldcat.org/oclc/840278135" target="_blank">https://search.worldcat.org/oclc/840278135</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">Khaleelulla 1982, pp. 103–110. - Khaleelulla, S. M. (1982). Counterexamples in Topological Vector Spaces. Lecture Notes in Mathematics. Vol. 936. Berlin, Heidelberg, New York: Springer-Verlag. ISBN 978-3-540-11565-6. OCLC 8588370. <a href="https://search.worldcat.org/oclc/8588370" target="_blank">https://search.worldcat.org/oclc/8588370</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
</ol>

DF-space open-in-new

DF-space