## Spaces in which compact sets have countable local bases

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- by Ralph R. Sabella
- Proc. Amer. Math. Soc.
**48**(1975), 499-504 - DOI: https://doi.org/10.1090/S0002-9939-1975-0370522-6
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## Abstract:

${D_1}$-spaces and coconvergent spaces are examples of spaces in which compact sets have countable local bases (${D_0}$-spaces). Among the results related to ${D_0}$-spaces given in this paper is a sufficient condition under which such spaces are coconvergent. In relation to a question posed by F. B. Jones, it is shown that a topological property sufficient for semimetrizable spaces to be developable is that they be coconvergent. Coconvergence implies metrizability in stratifiable spaces; it is shown in this paper that a ${D_0}$-space is metrizable if there exists a stratification satisfying a nesting-like condition.## References

- C. E. Aull,
*Closed set countability axioms*, Indag. Math.**28**(1966), 311–316. Nederl. Akad. Wetensch. Proc. Ser. A 69. MR**0199833** - Carlos J. R. Borges,
*On stratifiable spaces*, Pacific J. Math.**17**(1966), 1–16. MR**188982** - Jack G. Ceder,
*Some generalizations of metric spaces*, Pacific J. Math.**11**(1961), 105–125. MR**131860** - Geoffrey D. Creede,
*Concerning semi-stratifiable spaces*, Pacific J. Math.**32**(1970), 47–54. MR**254799**
R. W. Heath, - Ralph R. Sabella,
*Convergence properties of neighboring sequences*, Proc. Amer. Math. Soc.**38**(1973), 405–409. MR**312479**, DOI 10.1090/S0002-9939-1973-0312479-8
—,

*On certain first-countable spaces*, Ann. of Math. Studies, no. 60, Princeton Univ. Press, Princeton, N.J., 1965, pp. 103-113.

*Properties of neighboring sequences in stratifiable spaces*, Proc. Amer. Math. Soc. (submitted).

## Bibliographic Information

- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**48**(1975), 499-504 - MSC: Primary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370522-6
- MathSciNet review: 0370522