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Uniformization of quasi-uniform spaces

Published online by Cambridge University Press:  17 April 2009

T. G. Raghavan  and
I. L. Reilly
T. G. Raghavan
Affiliation:
Department of Mathematics, University of Auckland, Private Bag, Auckland, New Zealand.
I. L. Reilly
Affiliation:
Department of Mathematics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

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This paper considers the question of when a quasi-uniform space has a compatible uniform structure. Typical of the sufficient conditions provided is the result that a quasi-uniform space whose conjugate topology is compact and R0 is uniformizable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 413 - 422
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Fletcher, Peter, “Pairwise uniform spaces”, Abstract 65T–328, Notices Amer. Math. Soc. 12 (1965), 612.Google Scholar
[2]Fletcher, Peter, Hoyle, Hughes B. III, and Patty, C.W., “The comparison of topologies”, Duke Math. J. 36 (1969), 325–331.CrossRefGoogle Scholar
[3]Kelly, J.C., “Bitopological spaces”, Proc. London Math. Soc. (3) 13 (1963), 71–89.CrossRefGoogle Scholar
[4]Lane, E.P., “Bitopological spaces and quasi-uniform spaces”, Proc. London Math. Soc. (3) 17 (1967), 241–256.CrossRefGoogle Scholar
[5]Murdeshwar, M.G. and Naimpally, S.A., Quasi-uniform topological spaces (Noordhoff, Groningen, 1966).Google Scholar
[6]Patty, C.W., “Bitopological spaces”, Duke Math. J. 34 (1967), 387–391.CrossRefGoogle Scholar
[7]Pervin, William J., “Quasi-uniformization of topological spaces”, Math. Ann. 147 (1962), 316–317.CrossRefGoogle Scholar
[8]Raghavan, T.G. and Reilly, I.L., “Metrizability of quasi-metric spaces”, J. London Math. Soc. (2) 15 (1977), 169–172.CrossRefGoogle Scholar