Finite Intervals in the Lattice of Topologies

D.W. McIntyre

Abstract

We prove two basic facts about finite intervals in the lattice of
topologies on a set. One result states that a finite lattice is
isomorphic to an interval of topologies if and only if it is isomorphic
to an interval of topologies on a finite set, the other that not every
finite lattice is an interval of topologies, although every finite
lattice may be embedded into the lattice of topologies on a finite set.

Keywords
finite intervals of topologies, lattice of topologies, $M_3$

Math Review Classification
Primary 06B15, 54A10

Last Updated
21/4/97

Length
9 pages

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