Uniform spaces of countable type
Author:
Giovanni Vidossich
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- 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 https://doi.org/10.1090/S0002-9939-1961-0133108-4
- Giovanni Vidossich, Characterization of separability for ${\rm LF}$-spaces, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 87–90, vi (1969) (English, with French summary). MR 244733
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.30
Retrieve articles in all journals with MSC: 54.30
Additional Information
Keywords:
Uniform space,
uniform space of countable type,
injective space,
compact space,
<!– MATH ${\aleph _1}$ –> <IMG WIDTH="27" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\aleph _1}$">-reflection,
product and sum of uniform spaces,
function space,
uniform retraction,
countable uniform covering,
uniformly locally finite uniform covering,
star-refinement
Article copyright:
© Copyright 1970
American Mathematical Society