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Interior preserving maps

Published online by Cambridge University Press:  17 April 2009

T. Memp
T. Memp
Affiliation:
Gainesville, Florida, USA
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Abstract

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It is a curious fact that, while the functions which preserve closures are exactly the closed continuous functions, the interior-preserving functions form a much smaller class than the open continuous functions. In fact, the interior-preserving maps are essentially homeomorphisms, surjections between discrete spaces, and “sums” of these.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 209 - 212
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Dugundji, James, Topology (Allyn and Bacon, Boston, 1966).Google Scholar