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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