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A characterization for the products of $ k$- and $ \aleph \sb{0}$-spaces and related results


Author: Yoshio Tanaka
Journal: Proc. Amer. Math. Soc. 59 (1976), 149-155
MSC: Primary 54E35; Secondary 54B10, 54D50
DOI: https://doi.org/10.1090/S0002-9939-1976-0415580-6
MathSciNet review: 0415580
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Abstract: E. Michael introduced the notion of $ {\aleph _0}$-spaces and characterized spaces which are both $ k$-spaces and $ {\aleph _0}$-spaces (or, briefly, $ k$-and- $ {\aleph _0}$-spaces) as being precisely the quotient images of separable metric spaces.

The purpose of this paper is to give a necessary and sufficient condition for the product of two $ k$-and- $ {\aleph _0}$-spaces to be a $ k$-and- $ {\aleph _0}$-space. Moreover, as related matters, we shall consider the products of $ k$-spaces having other properties.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0415580-6
Keywords: Pseudobases, $ {\aleph _0}$-spaces, $ k$-networks, $ \aleph $-spaces, cosmic spaces, $ k$-spaces, strongly Fréchet spaces, $ M$-spaces, class $ \mathfrak{S}'$, class $ \mathfrak{T}'$
Article copyright: © Copyright 1976 American Mathematical Society