Article

Full entry | PDF   (0.1 MB)
Keywords:
bisequential spaces; filter base; s-map
Summary:
Weakly bisequential spaces were introduced by A.V. Arhangel'skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.
References:
[1] Arhangel'skii A.V.: Bisequential spaces, tightness of products, and metrizability conditions in topological groups. Trans. Moscow Math. Soc. 55 (1994), 207-219. MR 1468459
[2] Arhangel'skii A.V.: The frequency spectrum of a topological space and the product operation. Trans. Moscow Math. Soc. 40 (1981), 163-200.
[3] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers. Pacific J. Math. 113 (1984), 303-332. MR 0749538 | Zbl 0561.54016
[4] Foged L.: A characterization of closed images of metric spaces. Proc. Amer. Math. Soc. 95 (1985), 487-490. MR 0806093 | Zbl 0592.54027
[5] Junnila H.J.K., Yun Z.: $\aleph$-spaces and spaces with $\sigma$-hereditarily closure-preserving k-network. Topology Appl. 30 (1990), 209-215. MR 1173260
[6] Lin S.: Mapping theorems on $\aleph$-spaces. Topology Appl. 30 (1988), 159-164. MR 0967752 | Zbl 0663.54017
[7] Michael E.A.: A quintuple quotient quest. Topology Appl. 2 (1972), 91-138. MR 0309045 | Zbl 0238.54009
[8] Simon P.: A compact Fréchet space whose square is not Fréchet. Comment. Math. Univ. Carolinae 21 (1980), 749-753. MR 0597764 | Zbl 0466.54022
[9] Sirois-Dumais R.: Quasi- and weakly-quasi-first-countable space. Topology Appl. 11 (1980), 223-230. MR 0572376

Partner of