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Topological Spaces with a Unique Compatible Quasi-Uniformity

Published online by Cambridge University Press:  20 November 2018

W. F. Lindgren
W. F. Lindgren*
Affiliation:
Southern Illinois University, Carbondale, Illinois
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In [ 2 ] P. Fletcher proved that a finite topological space has a unique compatible quasi-uniformity; C. Barnhill and P. Fletcher showed in [1] that a topological space (X, ), with finite, has a unique compatible quasiuniformity. In this note we give some necessary conditions for unique quasiuniformizability.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 369 - 372
Copyright
Copyright © Canadian Mathematical Society 1971

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. Fletcher, P., Finite topological spaces and quasi-uniform structures, Canad. Math. Bull. 12 (1969), 771-775.Google Scholar
3. Fletcher, P., On completeness of quasi-uniform spaces, Arch. Math, (to appear).Google Scholar
4. Hunsaker, W. and Lindgren, W., Construction of quasi-uniformities. Math. Ann. 188 (1970), 39-42.Google Scholar
5. Lindgren, W., Uniquely quasi-uniformizable topological spaces, Arch. Math, (to appear).Google Scholar
6. Murdeshwar, M. G. and Naimpally, S. A., Quasi-uniform topological spaces, Noordhoff, Groningen, 1966.Google Scholar
7. Naimpally, S. A. and Warrack, B. D., Proximity spaces, Publ. Dept. Math., Univ. of Alberta, 1968.Google Scholar
8. Pervin, W. J., Quasi-uniformization of topological spaces. Math. Ann. 147 (1962), 316-317.Google Scholar
9. Pervin, W. J., Quasi-proximities for topological spaces, Math. Ann. 150 (1963), 325-326.Google Scholar