Geodesic
Quasi-Uniform Spaces and Topological Homeomorphism Groups(1)
Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 97-98

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a topological space and G a subgroup of the homeomorphism group H(X) with the topology of point-wise convergence. It is well-known that if X is uniformizable and G is equicontinuous with respect to a compatible uniformity then G is a topological group. In this paper we show that essentially this same result applies when X is only an R0-space (and hence in particular if X is T 1 or regular). A corresponding result for regular spaces has been proved [2]. 
Seyedin, Massood. Quasi-Uniform Spaces and Topological Homeomorphism Groups(1). Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 97-98. doi: 10.4153/CMB-1974-017-0
@article{10_4153_CMB_1974_017_0,
     author = {Seyedin, Massood},
     title = {Quasi-Uniform {Spaces} and {Topological} {Homeomorphism} {Groups(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {97--98},
     year = {1974},
     volume = {17},
     number = {1},
     doi = {10.4153/CMB-1974-017-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-017-0/}
}
TY  - JOUR
AU  - Seyedin, Massood
TI  - Quasi-Uniform Spaces and Topological Homeomorphism Groups(1)
JO  - Canadian mathematical bulletin
PY  - 1974
SP  - 97
EP  - 98
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-017-0/
DO  - 10.4153/CMB-1974-017-0
ID  - 10_4153_CMB_1974_017_0
ER  - 
%0 Journal Article
%A Seyedin, Massood
%T Quasi-Uniform Spaces and Topological Homeomorphism Groups(1)
%J Canadian mathematical bulletin
%D 1974
%P 97-98
%V 17
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-017-0/
%R 10.4153/CMB-1974-017-0
%F 10_4153_CMB_1974_017_0

[1] 1. Davis, A. S., Indexed systems of neighborhoods for general topological spaces, Amer. Math Monthly, 68 (1961), 886-893. Google Scholar

[2] 2. Fuller, R. V., Semiuniform spaces and topological homeomorphism groups, Proc. Amer. Math. Soc, 26 (1970), 365-368. Google Scholar

[3] 3. Murdeshwar, M. G. and Naimpally, S. A., Quasi-uniform topological spaces, Noordhoff (1966). Google Scholar

Cité par Sources :