HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES

Abstract

A function $f:X\rightarrow X$ determines a topology $P(f)$ on $X$ by taking the closed sets to be those sets $A\subseteq X$ with $f(A)\subseteq A$ . The topological space $(X,P(f))$ is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces.