Authors: V. I. Arnautov
Abstract
Let
X be a finite set and τ be a topology on
X which has precisely
m open sets. If
t(τ) is the number of possible one-point expansions of the topology τ on
Y=
X∪{
y}, then ({
m • (
m+3)} / {2})-1 ≥ t(τ) ≥ 2 •
m+
log2m-1 and ({
m • (
m+3)} / {2})-1 = t(τ) if and only if τ is a chain (i.e. it is a linearly ordered set) and
t(τ) =2 •
m+
log2m-1 if and only if τ is an atomistic lattice.
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