Developable spaces and nearness structures

Carlson, John W.

doi:10.1090/S0002-9939-1980-0556635-6

Developable spaces and nearness structures
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by John W. Carlson

Proc. Amer. Math. Soc. 78 (1980), 573-579

DOI: https://doi.org/10.1090/S0002-9939-1980-0556635-6

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Abstract:

Necessary and sufficient conditions on a nearness structure are provided for which the underlying topology is developable. It is also shown that a topology is developable if and only if it admits a compatible nearness structure with a countable base. Finally it is shown that a topological space is embeddable in a complete Moore space if and only if it admits a compatible nearness structure satisfying certain stated conditions. Moreover, the complete Moore space is homeomorphic to Herrlich’s completion of the space with the specified nearness structure.

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