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 if the following is satisfied: ``if is a hereditarily closure-preserving closed covering of such that each possesses the property , then possesses ". 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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DOI:
https://doi.org/10.1090/S0002-9939-1975-0383335-6

Keywords:
Closure-preserving,
hereditarily closure-preserving,
strongly hereditarily closure-preserving,
-locally finite,
-hereditarily closure-preserving,
-strongly hereditarily closure-preserving

Article copyright:
© Copyright 1975
American Mathematical Society