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Proceedings of the American Mathematical Society

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



On the closure-preserving sum theorem

Authors: M. K. Singal and Shashi Prabha Arya
Journal: Proc. Amer. Math. Soc. 53 (1975), 518-522
MSC: Primary 54B99
MathSciNet review: 0383335
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Abstract: The closure-preserving sum theorem holds for a property $ \mathcal{P}$ if the following is satisfied: ``if $ \{ {F_\alpha }:\alpha \epsilon \Omega \} $ is a hereditarily closure-preserving closed covering of $ X$ such that each $ {F_\alpha }$ possesses the property $ \mathcal{P}$, then $ X$ possesses $ \mathcal{P}$". A general technique for proving this theorem is developed. The theorem is shown to hold for a large number of topological properties. As an application, three general sum theorems have also been obtained.

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Keywords: Closure-preserving, hereditarily closure-preserving, strongly hereditarily closure-preserving, $ \sigma $-locally finite, $ \sigma $-hereditarily closure-preserving, $ \sigma $-strongly hereditarily closure-preserving
Article copyright: © Copyright 1975 American Mathematical Society