Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity |
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| Authors: | R E Hodel |
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| Institution: | Mathematics Department, Duke University, Durham, NC 27708, USA |
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| Abstract: | We use neighborhood assignments and cardinal functions to give a unified approach to metrizability and uniformity. This leads to a number of characterizations of m(X), the metrizability degree of X, u(X), the uniform weight of X, and w(X), the weight of X. For X normal (and regular), m(X) = u(X); it is unknown whether this result extends to completely regular spaces. |
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| Keywords: | Metrization theorem Uniform and quasi-uniform spaces Quasi-proximity and proximity spaces Totally bounded uniformity Symmetrizable spaces Cardinal functions Weight Metrizability degree Uniform weight |
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