Uniform spaces of countable type
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- by Giovanni Vidossich
- Proc. Amer. Math. Soc. 25 (1970), 551-553
- DOI: https://doi.org/10.1090/S0002-9939-1970-0261546-3
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Abstract:
Uniform spaces of countable type are uniform spaces having a basis of countable uniform coverings. The present note investigates some of their properties. It is proved the existence of uniformly locally finite uniform refinements, the separability of some of their function spaces and that an injective space of countable type whose points are intersections of at most ${2^{{\aleph _0}}}$ open sets must be separable.References
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
- Ernest Michael, On a theorem of Rudin and Klee, Proc. Amer. Math. Soc. 12 (1961), 921. MR 133108, DOI 10.1090/S0002-9939-1961-0133108-4
- Giovanni Vidossich, Characterization of separability for $\textrm {LF}$-spaces, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 87–90, vi (1969) (English, with French summary). MR 244733
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 551-553
- MSC: Primary 54.30
- DOI: https://doi.org/10.1090/S0002-9939-1970-0261546-3
- MathSciNet review: 0261546