Sets and Ordered Structures

Indexed in: Scopus, Zentralblatt MATH, EBSCO

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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Representation Theory

Pp. 163-210 (48)

DOI: 10.2174/978160805338411201010163

Author(s): Sergiu Rudeanu


The title of this chapter summarizes three types of representation theorems dealt with: representations of the elements of certain lattices as meets/joins of elements from prescribed subsets, isomorphic representation of several types of posets (semilattices, lattices) as posets (semilattices, lattices) of sets with inclusion as partial order, and finally a more sophisticated development of the latter representations in the case of distributive and Boolean lattices: the duality between these categories and certain categories of topological spaces. These types of problems are treated in §§ 2, 3 and 5, respectively. The first section is devoted to ideals and filters both as a preparation to the subsequent sections and in view of the numerous other applications. The topological prerequisites necessary to §5 are collected in §4.


Ideal, filter, prime filter, maximal filter, irreducibility, decomposition, set-theoretical embedding, clopen set, Stone space, homomorphism, Priestley space, Priestley duality.