Fréchet lattice

<h2 id="properties">Properties</h2>
<p>Every Fréchet lattice is a <a href="/facts/Locally_convex_vector_lattice/T6c39Lac">locally convex vector lattice</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> 
The set of all <a href="/facts/Weak_order_unit/SGs8PzII">weak order units</a> of a <a href="/facts/Separable_space/2bmU73bk">separable</a> Fréchet lattice is a dense subset of its positive cone.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> 
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<h2 id="examples">Examples</h2>
<p>Every <a href="/facts/Banach_lattice/pCPSsndf">Banach lattice</a> is a Fréchet lattice. 
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<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Banach_lattice/pCPSsndf">Banach lattice</a> – Banach space with a compatible structure of a lattice</li>
<li><a href="/facts/Locally_convex_vector_lattice/T6c39Lac">Locally convex vector lattice</a></li>
<li><a href="/facts/Join_and_meet/cYcLhRIR">Join and meet</a> – Concept in order theory</li>
<li><a href="/facts/Normed_lattice/zreeqV8e">Normed lattice</a></li>
<li><a href="/facts/Vector_lattice/FX7Mwfxe">Vector lattice</a> – Partially ordered vector space, ordered as a latticePages displaying short descriptions of redirect targets</li></ul>

<h2 id="bibliography">Bibliography</h2>
<ul><li>Narici, Lawrence; Beckenstein, Edward (2011). <i>Topological Vector Spaces</i>. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1584888666. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/144216834">144216834</a>.</li>
<li><a href="/facts/Helmut_H._Schaefer/xorHTDBE">Schaefer, Helmut H.</a>; Wolff, Manfred P. (1999). <i>Topological Vector Spaces</i>. <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></ul>

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

<ol>
<li id="fn:1"><p>Schaefer & Wolff 1999, pp. 234–242. - 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></p></li>
<li id="fn:2"><p>Schaefer & Wolff 1999, pp. 234–242. - 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></p></li>
<li id="fn:3"><p>Schaefer & Wolff 1999, pp. 234–242. - 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></p></li>
</ol>

Fréchet lattice open-in-new

Fréchet lattice