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Di Concilio, A.; Naimpally, S. A.

Uniform continuity in sequentially uniform spaces. (English) Zbl 0819.54014

Acta Math. Hung. 61, No. 1-2, 17-19 (1993).
The authors prove that every uniformly sequential uniform space is proximally fine, i.e., it is the finest uniform space inducing its proximity (no references to this result are given; it was proved e.g. by N. S. Ramm and A. S. Shvarts [Mat. Sb., Nov. Ser. 33(75), 157-180 (1952; Zbl 0050.391)]). Two consequences are given describing when a uniformly sequential space is topologically fine (both consequences, except the fourth condition in the second one, are valid for any proximally fine space).
Reviewer: M.Hušek (Praha)

Cited in 2 Documents

MSC:

54E15 Uniform structures and generalizations

Keywords:

uniformly sequential space; proximally fine space

Citations:

Zbl 0050.391
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\textit{A. Di Concilio} and \textit{S. A. Naimpally}, Acta Math. Hung. 61, No. 1--2, 17--19 (1993; Zbl 0819.54014)
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References:

[1] M. Atsuji, Uniform continuity of continuous functions of metric spaces,Pacific J. Math.,8 (1958), 11–16. · Zbl 0082.16207
[2] G. Beer, Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance,Proc. Amer. Math. Soc.,95 (1985), 653–658. · Zbl 0594.54007
[3] A. Di Concilio and S. A. Naimpally, Atsuji spaces: continuity versus uniform continuity, inProc. of VI. Brazilian Topology Meeting, Campinas, Sao Paolo, August, 1988.
[4] M. Hušek, Sequential uniform spaces,Proceedings of the Conference on Convergences, Bechyne, Czechoslovakia, 1984, pp. 177–188.
[5] S. A. Naimpally and B. D. Warrack,Proximity Spaces, Cambridge University Press, 1970.
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