L-Realcompactifications as Epireflections

If L is a countably productive normal base on a Tychonoff space X, then η(X, L) is an L*-realcompact extension of X. R. A. Alo and H. L. Shapiro thus generalized the Hewitt realcompactification of X. In the following paper, we extend this construction to T1-spaces and show that it is an epireflectio...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1974-05, Vol.44 (1), p.196-202
Main Authors: Bentley, H. L., Naimpally, S. A.
Format: Article
Language:English
Subjects:
Compactification
Contiguity
Functors
General topology
Marital property
Mathematical rings
Mathematical theorems
Topological spaces
Tychonoff spaces
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Summary:If L is a countably productive normal base on a Tychonoff space X, then η(X, L) is an L*-realcompact extension of X. R. A. Alo and H. L. Shapiro thus generalized the Hewitt realcompactification of X. In the following paper, we extend this construction to T1-spaces and show that it is an epireflection functor on an appropriate category. We are thus concerned with the question of the extendibility of a continuous map f: X → Y to a continuous map g: η(X, LX) → η(Y, LY). We derive necessary and sufficient conditions therefor in the case when LYis a nest generated intersection ring on Y.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1974-0365489-X