Geodesic
On spaces with point-countable $k$-systems
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 749-765
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper deals with the behavior of $M$-spaces, countably bi-quasi-$k$-spaces and singly bi-quasi-$k$-spaces with point-countable $k$-systems. For example, we show that every $M$-space with a point-countable $k$-system is locally compact paracompact, and every separable singly bi-quasi-$k$-space with a point-countable $k$-system has a countable $k$-system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael's paper [15] when the spaces have point-countable $k$-systems.
This paper deals with the behavior of $M$-spaces, countably bi-quasi-$k$-spaces and singly bi-quasi-$k$-spaces with point-countable $k$-systems. For example, we show that every $M$-space with a point-countable $k$-system is locally compact paracompact, and every separable singly bi-quasi-$k$-space with a point-countable $k$-system has a countable $k$-system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael's paper [15] when the spaces have point-countable $k$-systems.
Classification : 54D55, 54E18, 54E35
Keywords: countably-bi-quasi-$k$-space; point-countable $k$-system; local compactness; \newline metrizability 
@article{CMUC_2004_45_4_a15,
     author = {Yoshioka, Iwao},
     title = {On spaces with point-countable $k$-systems},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {749--765},
     year = {2004},
     volume = {45},
     number = {4},
     mrnumber = {2103090},
     zbl = {1099.54025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2004_45_4_a15/}
}
TY  - JOUR
AU  - Yoshioka, Iwao
TI  - On spaces with point-countable $k$-systems
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2004
SP  - 749
EP  - 765
VL  - 45
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMUC_2004_45_4_a15/
LA  - en
ID  - CMUC_2004_45_4_a15
ER  - 
%0 Journal Article
%A Yoshioka, Iwao
%T On spaces with point-countable $k$-systems
%J Commentationes Mathematicae Universitatis Carolinae
%D 2004
%P 749-765
%V 45
%N 4
%U http://geodesic.mathdoc.fr/item/CMUC_2004_45_4_a15/
%G en
%F CMUC_2004_45_4_a15
Yoshioka, Iwao. On spaces with point-countable $k$-systems. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 749-765. http://geodesic.mathdoc.fr/item/CMUC_2004_45_4_a15/