Nonstandard analysis of uniform spaces

S. Alagu, R. Kala

Abstract


There are nonstandard characterizations of classical topological concepts like total boundedness, completeness, comapactness etc., in metric spaces. In this article we present nonstandard extensions of these characterizations to uniform spaces. We also furnish completion of uniform spaces. We accomplish this by extending the methods in metric spaces by way of passing from sequences to filters and nets.

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Published: 2021-01-20

How to Cite this Article:

S. Alagu, R. Kala, Nonstandard analysis of uniform spaces, J. Math. Comput. Sci., 11 (2021), 1053-1062

Copyright © 2021 S. Alagu, R. Kala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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