Lattice representation by closed sets of a topological space
Fast, Richard H.
Fast, Richard H.
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1967-06-01
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Abstract
The purpose of this paper is to examine lattice
isomorphisms between abstract lattices and set lattice~.
In particular we are interested in lattices which are
lattice isomorphic to the lattice of closed sets of a topological
space. The main result is the construction of a
family of non-homeomorphic topological spaces which are
lattice isomorphic to a complete distributive lattice.
We will also obta1n a necessary and sufficient condition
for such a lattice -to have a topological representation,
and several restrictions on the number of spaces in the
representation family.
Table of Contents
Table of contents -- Introduction -- Preliminaries -- Topological representations -- Construction of a representation family -- Permissible closures -- Cardinality of the representation family -- References
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Thesis (M.S.)-- Wichita State Universtiy, College of Liberal Arts and Sciences, Dept. of Mathematics
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Wichita State University
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Wichita State University