A nontrivial T1-space admitting a unique quasi-proximity
Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 207-213

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

We construct a T1-space that is not hereditarily compact, although each of its open sets is the intersection of two compact open sets. The search for such a space was motivated by a problem in the theory of quasi-proximities.
Künzi, Hans-Peter A.; Watson, Stephen. A nontrivial T1-space admitting a unique quasi-proximity. Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 207-213. doi: 10.1017/S0017089500031451
@article{10_1017_S0017089500031451,
     author = {K\"unzi, Hans-Peter A. and Watson, Stephen},
     title = {A nontrivial {T1-space} admitting a unique quasi-proximity},
     journal = {Glasgow mathematical journal},
     pages = {207--213},
     year = {1996},
     volume = {38},
     number = {2},
     doi = {10.1017/S0017089500031451},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500031451/}
}
TY  - JOUR
AU  - Künzi, Hans-Peter A.
AU  - Watson, Stephen
TI  - A nontrivial T1-space admitting a unique quasi-proximity
JO  - Glasgow mathematical journal
PY  - 1996
SP  - 207
EP  - 213
VL  - 38
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500031451/
DO  - 10.1017/S0017089500031451
ID  - 10_1017_S0017089500031451
ER  - 
%0 Journal Article
%A Künzi, Hans-Peter A.
%A Watson, Stephen
%T A nontrivial T1-space admitting a unique quasi-proximity
%J Glasgow mathematical journal
%D 1996
%P 207-213
%V 38
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500031451/
%R 10.1017/S0017089500031451
%F 10_1017_S0017089500031451

[1] 1.Brümmer, G. C. L. and Künzi, H. P. A., Sobrification and bicompletion of totally bounded quasi–uniform spaces, Math. Proc. Camb. Phil. Soc. 101 (1987), 237–247. Google Scholar

[2] 2.Ferrer, J., On topological spaces with a unique quasi-proximity, Quaestiones Math. 17 (1994), 479–486. Google Scholar | DOI

[3] 3.Fletcher, P. and Lindgren, W. F., Quasi-uniform spaces (Dekker, 1982). Google Scholar

[4] 4.Künzi, H. P. A., Topological spaces with a unique compatible quasi-proximity, Arch. Math. 43 (1984), 559–561. Google Scholar | DOI

[5] 5.Künzi, H. P. A., Some remarks on quasi-uniform spaces, Glasgow Math. J. 31 (1989), 309–320. Google Scholar | DOI

[6] 6.Künzi, H. P. A., Quasi-uniform spaces—eleven years later, Topology Proc. 18 (1993), 143–171. Google Scholar

[7] 7.Lindgren, W. F., Topological spaces with a unique compatible quasi-uniformity, Canad. Math. Bull. 14 (1971), 369–372. Google Scholar | DOI

[8] 8.Lindgren, W. F., Topological spaces with unique quasi–uniform structure, Arch. Math. 22 (1971), 417–419. Google Scholar | DOI

[9] 9.Stone, A. H., Hereditarily compact spaces, Amer. J. Math. 82 (1960), 900–916. Google Scholar | DOI

Cité par Sources :