Compact $\sigma$-metric Hausdorff spaces are sequential
HTML articles powered by AMS MathViewer
- by A. J. Ostaszewski PDF
- Proc. Amer. Math. Soc. 68 (1978), 339-343 Request permission
Abstract:
It is shown that a locally countably compact, regular ${T_2}$ space which may be covered by a countable number of metrizable subspaces is sequential.References
-
A. V. Arhangel’skiÄ, Suslin number and cardinality. Characters of points in sequential bicompacta, Soviet Math. Dokl. 11 (1970), 597-601.
—, The closed image of a metric space can be condensed to a metric space, Soviet Math. Dokl. 7 (1966), 1109-1112.
- A. V. Arhangel′skiÄ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115–162. MR 0227950, DOI 10.1070/RM1966v021n04ABEH004169
- A. V. Arhangel′skiÄ and S. P. Franklin, Ordinal invariants for topological spaces, Michigan Math. J. 15 (1968), 313-320; addendum, ibid. 15 (1968), 506. MR 0240767
- S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 180954, DOI 10.4064/fm-57-1-107-115
- V. Kannan, Ordinal invariants in topology. I. On two questions of Arhangel′skiÄ and Franklin, General Topology and Appl. 5 (1975), no. 4, 269–296. MR 394574, DOI 10.1016/0016-660X(75)90001-X
- A. J. Ostaszewski, On countably compact, perfectly normal spaces, J. London Math. Soc. (2) 14 (1976), no. 3, 505–516. MR 438292, DOI 10.1112/jlms/s2-14.3.505
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 339-343
- MSC: Primary 54D55
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467677-4
- MathSciNet review: 0467677