Article
Keywords:
metric spaces; $g$-metrizable spaces; 1-sequence-covering mappings; $\sigma $-mappings; quotient mappings
Summary:
In this paper, the relationships between metric spaces and $g$-metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
References:
[1] P. Alexandroff:
On some results concerning topological spaces and their continuous mappings. In: Proc. Symp. Gen. Top. (Prague, 1961), 1961, pp. 41–54.
MR 0145472
[3] Shou Lin:
On sequence-covering $s$-mappings. Adv. Math. (China) 25 (1996), 548–551.
MR 1453163
[4] Shou Lin: $\sigma $-mappings and Alexandroff’s problems. (to appear).
[5] J. R. Boone and F. Siwiec:
Sequentially quotient mappings. Czechoslovak Math. J. 26 (1976), 174–182.
MR 0402689
[7] A. V. Arhangel’skii:
Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162.
MR 0227950
[8] Y. Tanaka:
$\sigma $-hereditarily closure-preserving $k$-networks and $g$-metrizability. Proc. Amer. Math. Soc. 112 (1991), 283–290.
MR 1049850 |
Zbl 0770.54031