A Property Between Compact and Strongly Countably Compact
Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 193
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
In this paper we consider a class of spaces called
hypercountably compact (hcc)spaces. The class of countably compact and the
class of strongly countably compact (scc) spaces contain the class of
hypercountably compact spaces. In example 2.1, we give a strongly countably
compact space which is not hypercountably compact. In the class of spaces
satisfying the first axiom of countability the notions hcc and scc coincide
(Theorem 2.3). Some equivalent conditions for a space to be hcc are given
in Theorem 2.2. The hcc property is not a continuous invariant (Example 2.4).
In section 3 we consider compact spaces which contain noncompact hcc (scc)
spaces as subspaces. In section 4 we also consider strongly sequentially
compact (ssc) spaces.
Classification :
54D30 54820
@article{PIM_1985_N_S_38_52_a24,
author = {Du\v{s}an Milovan\v{c}evi\'c},
title = {A {Property} {Between} {Compact} and {Strongly} {Countably} {Compact}},
journal = {Publications de l'Institut Math\'ematique},
pages = {193 },
publisher = {mathdoc},
volume = {_N_S_38},
number = {52},
year = {1985},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a24/}
}
Dušan Milovančević. A Property Between Compact and Strongly Countably Compact. Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 193 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a24/