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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Regular closed maps

Author: R. F. Dickman
Journal: Proc. Amer. Math. Soc. 39 (1973), 414-416
MSC: Primary 54C10
MathSciNet review: 0315654
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Abstract: A subset $ A$ of $ X$ is far from the remainder if whenever $ \mathcal{U}$ is a free open ultrafilter in $ X$ there exists $ U \in \mathcal{U}$ such that $ A \cap {\text{c}}{{\text{l}}_X}U = \emptyset $. A map is regular closed provided that the image of every regular closed set is closed. In this note we use some recent results of G. Viglino to show that every map can be extended to a regular closed map with far from the remainder point inverses. We also relate these maps to several other interesting classes of maps.

References [Enhancements On Off] (What's this?)

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Keywords: Regular closed maps, absolutely closed maps
Article copyright: © Copyright 1973 American Mathematical Society

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