Continuous functions on extremally disconnected spaces

J. Vermeer
1995 Transactions of the American Mathematical Society  
Using results and techniques due to Abramovich, Arenson and Kitover it is shown that each fixed-point set of a selfmap of a compact extremally disconnected space is a retract of that space, and that the retraction can be constructed from the particular selfmap itself. Also, the closure of the set of periodic points turns out to be a retract of the space. Several decomposition theorems for arbitrary selfmaps on extremally disconnected spaces are obtained similar to the theorem of Frolik on
more » ... ings. Conditions are obtained under which the set of fixed points is clopen.
doi:10.1090/s0002-9947-1995-1311920-0 fatcat:tsomdomtnbfezhmwojdagc2rgy