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Dense Subspaces of Product Spaces

Published online by Cambridge University Press:  20 November 2018

Toshiji Terada
Toshiji Terada*
Affiliation:
Yokohama National University, Hodogaya, Yokohama, Japan
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Unless otherwise specified, all spaces considered here are regular T1-spaces. A space X is called σ-discrete if X is the union of a countable family of discrete subspaces. Arhangel'skii [2] showed that the class of spaces which contain dense σ-discrete subspaces is productive. The fact that the class of spaces which contain dense subspaces of countable pseudocharacter is productive is obtained by Amirdzanov [1]. On the other hand, the class of spaces which contain metrizable spaces as dense subspaces is obviously not productive. As a generalized concept of metrizable spaces there is the concept of σ-spaces [14]. This class of spaces has many similar properties to the class of metrizable spaces. However we will point out a remarkable difference between the class of metrizable spaces and the class of σ-spaces by showing that the class of spaces which contain σ-spaces as dense subspaces is productive.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 6 , 01 December 1983 , pp. 986 - 1000
Copyright
Copyright © Canadian Mathematical Society 1983

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