Sets and Ordered Structures

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This e-book presents several basic methods and results of order theory that are currently used in various branches of mathematics. It presents topics that require a broad explanation in a concise and ...
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Applications

Pp. 211-240 (30)

Sergiu Rudeanu

Abstract

We have selected in five chapters what we believe to be the core of sets and order in mathematics. Of course,we are aware that this was an ambitious plan and that our selection could not be infallible. Yet we did our best and we conclude the eBook with several examples which illustrate the applications of lattices to topology (§§1-3), to universal algebra (§4), to a new field of applied mathematics called formal concept analysis (§5) and to logic (§6). Besides the references to the literature given in the sections of this chapter, we recommend a nice paper by Birkhoff [1970], with the suggestive title “What can lattices do for you?”.

Keywords:

Closure algebra, topological closure, almost discrete space, Heyting algebra, algebraic lattice, equivalence lattice, congruence lattice, formal context, formal concept, Lindenbaum-Tarski algebra, completeness theorem.

Affiliation:

University of Bucharest, Romania