Cardinal functions for $k$-spaces
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- by James R. Boone, Sheldon W. Davis and Gary Gruenhage
- Proc. Amer. Math. Soc. 68 (1978), 355-358
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467676-2
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Abstract:
In this paper, four cardinal functions are defined on the class of k-spaces. Some of the relationships between these cardinal functions are studied. Characterizations of various k-spaces are presented in terms of the existence of these cardinal functions. A bound for the ordinal invariant $\kappa$ of Arhangelskii and Franklin is established in terms of the tightness of the space. Examples are presented which exhibit the interaction between these cardinal invariants and the ordinal invariants of Arhangelskii and Franklin.References
- Richard Arens, Note on convergence in topology, Math. Mag. 23 (1950), 229–234. MR 37500, DOI 10.2307/3028991
- A. V. Arhangel′skiĭ, The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR 187 (1969), 967–970 (Russian). MR 0251695
- A. V. Arhangel′skiĭ and S. P. Franklin, Ordinal invariants for topological spaces, Michigan Math. J. 15 (1968), 313–320; addendum, ibid. 15 (1968), 506. MR 0240767 S. W. Davis, A study of certain classes of isocompact spaces and of the relationships among them, Dissertation, Ohio University, 1976.
- S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 180954, DOI 10.4064/fm-57-1-107-115
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 355-358
- MSC: Primary 54D50; Secondary 54A25
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467676-2
- MathSciNet review: 0467676