Geodesic
On compact $T_1$-spaces
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 20-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider spaces, any subspaces of which are compact. We call such spaces hereditarily compact. The present work covers questions on the existence and methods of constructing hereditarily compact $T_1$-topologies. We prove the existence of $2^\tau$ pairwise incomparable hereditarily compact $T_1$-topologies on an infinite set $X$ of power $\tau$. The characteristics of hereditarily compact spaces are obtained. It is proved that the Tychonoff product of a finite number of hereditarily compact $T_1$-spaces is a hereditarily compact $T_1$-space, but the Tychonoff product of an infinite number of nonsingleton hereditarily compact $T_1$-spaces is not hereditarily compact.
Keywords: compactness, minimal $T_1$-topology, Tychonoff product. 
@article{VUU_2013_3_a1,
     author = {M. E. Voronov},
     title = {On compact $T_1$-spaces},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {20--27},
     year = {2013},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_3_a1/}
}
TY  - JOUR
AU  - M. E. Voronov
TI  - On compact $T_1$-spaces
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2013
SP  - 20
EP  - 27
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2013_3_a1/
LA  - ru
ID  - VUU_2013_3_a1
ER  - 
%0 Journal Article
%A M. E. Voronov
%T On compact $T_1$-spaces
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2013
%P 20-27
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2013_3_a1/
%G ru
%F VUU_2013_3_a1
M. E. Voronov. On compact $T_1$-spaces. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 20-27. http://geodesic.mathdoc.fr/item/VUU_2013_3_a1/

[1] de Groot Y., “An isomorphism principle in general topology”, Bull. Amer. Math. Soc., 73:3 (1967), 465–467 | DOI | MR | Zbl

[2] Arkhangel'skii A. V., “Maps and spaces”, Usp. Mat. Nauk, 21:4 (1966), 133–184 | MR | Zbl

[3] Arkhangel'skii A. V., Ponomarev V. I., Funda-mentals of general topology through problems and exercises, Nauka, Moscow, 1974, 424 pp. | MR

[4] Engelking R., General topology, Mir, Moscow, 1986, 752 pp. | MR

[5] Fedorchuk V. V., Filippov V. V., General topology. Basic design, Fizmatlit, Moscow, 2006, 336 pp.