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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0261546-3
Keywords: Uniform space, uniform space of countable type, injective space, compact space, $ {\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