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A Note on Locally Quasi-Uniform Spaces

Published online by Cambridge University Press:  20 November 2018

Troy L. Hicks  and
Shirley M. Huffman
Troy L. Hicks
Affiliation:
Department of Mathematics, University of Missouri-RollaRolla, Missouri65401
Shirley M. Huffman
Affiliation:
Department of Mathematics, Southwest Missouri State UniversitySpringfield, Missouri65802
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Abstract

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Locally quasi-uniform spaces are studied, and it is shown that a topological space (X, t) admits exactly one compatible locally quasi-uniform structure if and only if t is finite.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 501 - 504
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Barnhill, C. and Fletcher, P., Topological spaces with a unique compatible quasi-uniform structure, Arch. Math. 21 (1970), 206–209.Google Scholar
2. Doss, R., On uniform spaces with a unique structure, Amer. J. Math. 71 (1949), 19–23.Google Scholar
3. Fletcher, P., Finite topological spaces and quasi-uniform structures, Canad. Math. Bull. 12 (1969), 771–775.Google Scholar
4. Fletcher, P. and Lindgren, W., Transitive quasi-uniformities, J. Math. Anal. Appl. 39 (1972) 397–405.Google Scholar
5. Lindgren, W. and Fletcher, P., Locally quasi-uniform spaces with countable bases, Duke Math. J. 41 (1974), 231–240.Google Scholar
6. Lindgren, W., Topological spaces with a unique compatible quasi-uniformity, Canad. Math. Bull. 14 (1971), 369–372.Google Scholar
7. Lindgren, W., Topological spaces with unique quasi-uniform structure, Arch. Math. 22 (1971), 417–419.Google Scholar
8. Murdeshwar, M. G. and Naimpally, S. A., Quasi-uniform Spaces, P. Noordhoff Ltd., Groningen, (1966).Google Scholar