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.
@article{119390,
author = {Yoshio Tanaka},
title = {Products of $k$-spaces, and questions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {44},
year = {2003},
pages = {335-345},
zbl = {1100.54006},
mrnumber = {2026168},
language = {en},
url = {http://dml.mathdoc.fr/item/119390}
}
Tanaka, Yoshio. Products of $k$-spaces, and questions. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 335-345. http://gdmltest.u-ga.fr/item/119390/
Linear $s$-spaces, Proc. Symp. Convergent structures, Univ. Oklahoma, 1965.
Spaces in which sequences suffice, Fund. Math. LVII (1965), 107-113. (1965) | MR 0180954 | Zbl 0132.17802
Spaces determined by point-countable covers, Pacific J. Math. 113 (1984), 303-332. (1984) | MR 0749538 | Zbl 0561.54016
A note on the Arens' space and sequential fan, Topology Appl. 81 (1997), 185-196. (1997) | MR 1485766 | Zbl 0885.54019
On spaces with point-countable $cs$-networks, Topology Appl. 74 (1996), 51-60. (1996) | MR 1425925 | Zbl 0869.54036
Bi-quotient maps and cartesian products of quotient maps, Ann. Inst. Fourier, Grenoble 18 (1968), 287-302. (1968) | MR 0244964 | Zbl 0175.19704
A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91-138. (1972) | MR 0309045 | Zbl 0238.54009
$A$-spaces and countably bi-quotient maps, Dissertationes Math. 133 (1976), 4-43. (1976) | MR 0418023 | Zbl 0338.54006
Strongly sequential spaces, Comment. Math. Univ. Carolinae 41 (2000), 143-153. (2000) | MR 1756935 | Zbl 1037.54504
More on strongly sequential spaces, Comment. Math. Univ. Carolinae 43 (2002), 525-530. (2002) | MR 1920528 | Zbl 1090.54006
Bi-quotient maps, countably bi-sequential spaces, and related topics, Gen. Topology Appl. 4 (1974), 1-28. (1974) | MR 0365463 | Zbl 0278.54008
Sequence-converging and countably bi-quotient mappings, Gen. Topology Appl. 1 (1971), 143-154. (1971) | MR 0288737
On products of quasi-perfect maps, Proc. Japan Acad. 46 (1970), 1070-1073. (1970) | MR 0296917 | Zbl 0226.54008
On quasi-$k$-spaces, Proc. Japan Acad. 46 (1970), 1074-1079. (1970) | MR 0296887 | Zbl 0224.54030
On sequential spaces, Science Reports of Tokyo Kyoiku Daigaku Sect. A, 11 (1971), 68-72. (1971) | MR 0307172 | Zbl 0246.54026
Products of sequential spaces, Proc. Amer. Math. Soc. 54 (1976), 371-375. (1976) | MR 0397665 | Zbl 0292.54025
A characterization for the products of $k$-and-${\aleph}_0$-spaces and related results, Proc. Amer. Math. Soc. 59 (1976), 149-155. (1976) | MR 0415580 | Zbl 0336.54026
On the $k$-ness for the products of closed images of metric spaces, Gen. Topology Appl. 9 (1978), 175-183. (1978) | MR 0493934 | Zbl 0387.54010
Point-countable $k$-systems and products of $k$-spaces, Pacific J. Math. 101 (1982), 199-208. (1982) | MR 0671852 | Zbl 0498.54023
Metrizability of certain quotient spaces, Fund. Math. 119 (1983), 157-168. (1983) | MR 0731817
On the products of $k$-spaces questions, Questions Answers Gen. Topology 1 (1983), 36-50. (1983) | MR 0698037
$k$-spaces and the products of closed images, Questions Answers Gen. Topology 1 (1983), 88-99. (1983) | MR 0722087 | Zbl 0545.54021
Point-countable covers and $k$-networks, Topology Proc. 12 (1987), 327-349. (1987) | MR 0991759 | Zbl 0676.54035
Products of $k$-spaces having point-countable $k$-networks,, Topology Proc. 22 (1997), 305-329. (1997) | MR 1657891 | Zbl 0916.54017
Products of $k$-spaces, and special countable spaces, to appear in Tsukuba J. Math. | MR 2025736 | Zbl 1057.54022