Products of k -spaces, and questions

Yoshio Tanaka

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 2, page 335-345
  • ISSN: 0010-2628

Abstract

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As is well-known, every product of a locally compact space with a k -space is a k -space. But, the product of a separable metric space with a k -space need not be a k -space. In this paper, we consider conditions for products to be k -spaces, and pose some related questions.

How to cite

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Tanaka, Yoshio. "Products of $k$-spaces, and questions." Commentationes Mathematicae Universitatis Carolinae 44.2 (2003): 335-345. <http://eudml.org/doc/249188>.

@article{Tanaka2003,
abstract = {As is well-known, every product of a locally compact space with a $k$-space is a $k$-space. But, the product of a separable metric space with a $k$-space need not be a $k$-space. In this paper, we consider conditions for products to be $k$-spaces, and pose some related questions.},
author = {Tanaka, Yoshio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$k$-space; sequential space; strongly Fr’echet space; bi-$k$-space; strongly sequential space; Tanaka space; -space; strongly Fréchet space; bi--space; strongly sequential space; Tanaka space},
language = {eng},
number = {2},
pages = {335-345},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Products of $k$-spaces, and questions},
url = {http://eudml.org/doc/249188},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Tanaka, Yoshio
TI - Products of $k$-spaces, and questions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 2
SP - 335
EP - 345
AB - As is well-known, every product of a locally compact space with a $k$-space is a $k$-space. But, the product of a separable metric space with a $k$-space need not be a $k$-space. In this paper, we consider conditions for products to be $k$-spaces, and pose some related questions.
LA - eng
KW - $k$-space; sequential space; strongly Fr’echet space; bi-$k$-space; strongly sequential space; Tanaka space; -space; strongly Fréchet space; bi--space; strongly sequential space; Tanaka space
UR - http://eudml.org/doc/249188
ER -

References

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  24. Tanaka Y., Products of k -spaces having point-countable k -networks,, Topology Proc. 22 (1997), 305-329. (1997) Zbl0916.54017MR1657891
  25. Tanaka Y., Shimizu Y., Products of k -spaces, and special countable spaces, to appear in Tsukuba J. Math. Zbl1057.54022MR2025736

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