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Proceedings of the American Mathematical Society

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

 

 

Developable spaces and nearness structures


Author: John W. Carlson
Journal: Proc. Amer. Math. Soc. 78 (1980), 573-579
MSC: Primary 54E17; Secondary 54E30
DOI: https://doi.org/10.1090/S0002-9939-1980-0556635-6
MathSciNet review: 556635
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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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DOI: https://doi.org/10.1090/S0002-9939-1980-0556635-6
Keywords: Nearness space, developable, complete Moore space, extensions
Article copyright: © Copyright 1980 American Mathematical Society