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Duality theory for distributive lattices
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<h2 id="see-also">See also</h2> <ul><li><a href="/facts/Representation_theorem/Fu6DYyGD">Representation theorem</a></li> <li><a href="/facts/Birkhoff%27s_representation_theorem/Mg51p9wz">Birkhoff's representation theorem</a></li> <li><a href="/facts/Stone%27s_representation_theorem_for_Boolean_algebras/tN870P19">Stone's representation theorem for Boolean algebras</a></li> <li><a href="/facts/Stone_duality/w1QqNX39">Stone duality</a></li> <li><a href="/facts/Esakia_duality/ma7csbJC">Esakia duality</a></li></ul> <h2 id="notes">Notes</h2> <ul><li><a href="/facts/Hilary_Priestley/d8r8I53C">Priestley, H. A.</a> (1970). Representation of distributive lattices by means of ordered Stone spaces. <i>Bull. London Math. Soc.</i>, (2) 186–190.</li> <li>Priestley, H. A. (1972). Ordered topological spaces and the representation of distributive lattices. <i>Proc. London Math. Soc.</i>, 24(3) 507–530.</li> <li>Stone, M. (1938). <a href="https://eudml.org/doc/27235">Topological representation of distributive lattices and Brouwerian logics.</a> <i>Casopis Pest. Mat. Fys., 67 1–25.</i></li> <li>Cornish, W. H. (1975). On H. Priestley's dual of the category of bounded distributive lattices. <i>Mat. Vesnik</i>, 12(27) (4) 329–332.</li> <li>M. Hochster (1969). Prime ideal structure in commutative rings. <i>Trans. Amer. Math. Soc.</i>, 142 43–60</li> <li><a href="/facts/P._T._Johnstone/j3k2A3Xl">Johnstone, P. T.</a> (1982). <i>Stone spaces</i>. Cambridge University Press, Cambridge. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-23893-5.</li> <li>Jung, A. and Moshier, M. A. (2006). On the bitopological nature of Stone duality. <i>Technical Report CSR-06-13</i>, School of Computer Science, University of Birmingham.</li> <li>Bezhanishvili, G., Bezhanishvili, N., Gabelaia, D., Kurz, A. (2010). Bitopological duality for distributive lattices and Heyting algebras. <i>Mathematical Structures in Computer Science</i>, 20.</li> <li>Dickmann, Max; Schwartz, Niels; Tressl, Marcus (2019). <i>Spectral Spaces</i>. New Mathematical Monographs. Vol. 35. Cambridge: <a href="/facts/Cambridge_University_Press/fgEBSSRq">Cambridge University Press</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1017%2F9781316543870">10.1017/9781316543870</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9781107146723.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Stone (1938) <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Stone (1938), Johnstone (1982) <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Stone (1938), Johnstone (1982) <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Bezhanishvili et al. (2010) <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Priestley (1970) <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Bezhanishvili et al. (2010) <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> </ol>