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- W3022535420 abstract "A uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure that is used to define uniform properties, such as completeness, uniform continuity, and uniform convergence. A quasi-uniform space is quasi-metrizable if its quasi-uniformity has a countable base and every topological space is quasi-uniformizable. The interior of every member of a uniformity belongs to the uniformity so that every member of a uniformity is a neighborhood of the diagonal in the product topology induced by the uniformity. Furthermore, the family of closed symmetric members of the uniformity is also a base for the uniformity. Although every member of a uniformity is a neighborhood of the diagonal, the converse is not always true. In the usual metric uniformity for the reals, for example, not all neighborhoods of the diagonal belong to the uniformity." @default.
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- W3022535420 date "1964-01-01" @default.
- W3022535420 modified "2023-09-26" @default.
- W3022535420 title "Uniform Spaces" @default.
- W3022535420 doi "https://doi.org/10.1016/b978-1-4832-0012-5.50016-2" @default.
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