Semiuniform spaces and topological homeomorphism groups
Abstract: A well-known sufficient condition that a group of homeomorphisms, , from a topological space onto itself be a topological group relative to the topology of pointwise convergence is that be uniformizable and be equicontinuous.
In this paper we prove an analogous condition in which the space is assumed to be only regular instead of completely regular (uniformizable). This is accomplished by means of the concepts of semiuniformity and semiequicontinuity introduced here.
-  Nicolas Bourbaki, Elements of mathematics. General topology. Part 2, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205211
-  Taqdir Husain, Introduction to topological groups, W. B. Saunders Co., Philadelphia, Pa.-London, 1966. MR 0200383
-  S. K. Kaul, Compact subsets in function spaces, Canad. Math. Bull. 12 (1969), 461–466. MR 0257967, https://doi.org/10.4153/CMB-1969-057-9
-  John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
- Nicolas Bourbaki, Elements of mathematics. General topology. Part 2, Hermann, Paris and Addison-Wesley, Reading, Mass., 1966. MR 34 #5044b. MR 0205211 (34:5044b)
- Taqdir Husain, Introduction to topological groups, Saunders, Philadelphia, Pa., 1966. MR 34 #278. MR 0200383 (34:278)
- S. K. Kaul, Compact subsets in function spaces, Canad. Math. Bull. 12 (1969), 461-466. MR 0257967 (41:2616)
- John L. Kelley, General topology, Van Nostrand, Princeton, N. J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
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Keywords: Semiuniformity, semiequicontinuity, uniform semiuniformity, semitopological group
Article copyright: © Copyright 1970 American Mathematical Society