HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES.

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. [ABSTRACT FROM AUTHOR]