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Proceedings of the American Mathematical Society

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Products and remote points: examples and counterexamples


Authors: A. Dow and T. J. Peters
Journal: Proc. Amer. Math. Soc. 104 (1988), 1296-1304
MSC: Primary 54D40; Secondary 03E35, 03E55, 54B10, 54D35, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1988-0969061-X
MathSciNet review: 969061
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Abstract: Examples of products with remote points and counterexamples of products without remote points are given. The paradoxical behavior of remote points with respect to products is exhibited.

Also, an example is given of spaces $ X$ and $ Y$, where neither $ X$ nor $ Y$ has a $ \sigma $-locally finite $ \pi $-base, but $ X \times Y$ does.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0969061-X
Keywords: $ \beta X,\sigma $-locally finite $ \pi $-base, $ \sigma - \pi $ space, $ \pi $-base, infinitary combinatorics, nonpseudocompact, product, remainder, remote points, Stone-Čech compactification
Article copyright: © Copyright 1988 American Mathematical Society

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