Topology Atlas
Document # ppae-16

## Compactification of a map which is mapped to itself

### A. Iwanik, L. Janos and F. A. Smith

Proceedings of the Ninth Prague Topological Symposium
(2001)
pp. 165-169
We prove that if T:X --> X is a selfmap of a set X such that
\cap {T^{n}X:n `in` **N**} is a one-point set, then the set X can be
endowed with a compact Hausdorff topology so that T is continuous.

Mathematics Subject Classification. 54H20 54H25.

Keywords. Fixed Point Principle.

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Copyright © 2002
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Topology Atlas.
Published April 2002.