Geodesic
R 1, Pairwise Compact, and Pairwise Complete Spaces
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 109-113

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

The R 1 axiom was first introduced by Davis in [1]. It is strictly weaker than the T 2 axiom. Murdeshwar and Naimpally, in [4], have weakened the T 2 hypothesis to R1 in some well-known theorems. We show that in many topological spaces the R 1 axiom and regularity are equivalent. Also, the definition of local compactness given in [4] can be weakened to the usual definition and still get the same results.The notion of a bitopological space was first introduced by Kelley in [3]. Fletcher, Hoyle, and Patty discuss pairwise compactness for bitopological spaces in [2]. One of our main results is that a bitopological space (X, P, Q) is pairwise compact if and only if each ultrafilter v on X, containing a proper P closed set and a proper Q closed set, has a common P and Q limit. 
Richardson, G. D. R 1, Pairwise Compact, and Pairwise Complete Spaces. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 109-113. doi: 10.4153/CMB-1972-019-4
@article{10_4153_CMB_1972_019_4,
     author = {Richardson, G. D.},
     title = {R 1, {Pairwise} {Compact,} and {Pairwise} {Complete} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {109--113},
     year = {1972},
     volume = {15},
     number = {1},
     doi = {10.4153/CMB-1972-019-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-019-4/}
}
TY  - JOUR
AU  - Richardson, G. D.
TI  - R 1, Pairwise Compact, and Pairwise Complete Spaces
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 109
EP  - 113
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-019-4/
DO  - 10.4153/CMB-1972-019-4
ID  - 10_4153_CMB_1972_019_4
ER  - 
%0 Journal Article
%A Richardson, G. D.
%T R 1, Pairwise Compact, and Pairwise Complete Spaces
%J Canadian mathematical bulletin
%D 1972
%P 109-113
%V 15
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-019-4/
%R 10.4153/CMB-1972-019-4
%F 10_4153_CMB_1972_019_4

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

[2] 2. Fletcher, P., Hoyle, H. B., and Patty, C. W., The comparison of topologies, Duke Math. J. 36 (1969), 325-331. Google Scholar

[3] 3. Kelley, J. C., Bitopological spaces, Proc. Londo. Math. Soc. 13 (1963), 71-89. Google Scholar

[4] 4. Murdeshwar, M. G. and Naimpally, S. A., Rtopological spaces, Canad. Math. Bull. 9 (1966), 521-523. Google Scholar

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

Cité par Sources :