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fixed set property

A topological space X$ is said to have the fixed set property for a certain class C$ of maps of X$ onto itself provided there exists, for each non-empty closed set A$ in X$, a map f$ in C$ such that f(x) = x$ if and only if x$ is in A$.
next up previous contents index
Next: fixed point self-homeomorphic Up: Definitions Previous: fixed point
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30