Geodesic
Certain Subsets of Products of Metacompact Spaces and Subparacompact Spaces are Realcompact
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 825-829

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

We will say that a space X has property (*) if and only if each discrete subset of X is realcompact; i.e., the cardinality of each discrete subset of X is nonmeasurable. In [8], Shirota shows that a completely regular T 1-space X is realcompact if and only if X has property (*) and X is complete with respect to some uniformity. In [7], Moran, using measure theoretic techniques, shows that any normal metacompact T 1-space with property (*) is realcompact. 
Zenor, Phillip. Certain Subsets of Products of Metacompact Spaces and Subparacompact Spaces are Realcompact. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 825-829. doi: 10.4153/CJM-1972-081-9
@article{10_4153_CJM_1972_081_9,
     author = {Zenor, Phillip},
     title = {Certain {Subsets} of {Products} of {Metacompact} {Spaces} and {Subparacompact} {Spaces} are {Realcompact}},
     journal = {Canadian journal of mathematics},
     pages = {825--829},
     year = {1972},
     volume = {24},
     number = {5},
     doi = {10.4153/CJM-1972-081-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-081-9/}
}
TY  - JOUR
AU  - Zenor, Phillip
TI  - Certain Subsets of Products of Metacompact Spaces and Subparacompact Spaces are Realcompact
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 825
EP  - 829
VL  - 24
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-081-9/
DO  - 10.4153/CJM-1972-081-9
ID  - 10_4153_CJM_1972_081_9
ER  - 
%0 Journal Article
%A Zenor, Phillip
%T Certain Subsets of Products of Metacompact Spaces and Subparacompact Spaces are Realcompact
%J Canadian journal of mathematics
%D 1972
%P 825-829
%V 24
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-081-9/
%R 10.4153/CJM-1972-081-9
%F 10_4153_CJM_1972_081_9

[1] 1. Burke, D. K., On subparacompact spaces, Proc. Amer. Math. Soc. 23 (1969), 655–663. Google Scholar

[2] 2. Creede, G., Semi-stratifiable spaces, Topology Conference, Ariz. State Univ., Tempe, Ariz. (1967), 318–324. Google Scholar

[3] 3. Gillman, L. and Jerison, M., Rings of continuous functions (VanNostrand, Princeton, 1960). Google Scholar

[4] 4. Kelley, J., General topology (VanNostrand, Princeton, 1955). Google Scholar

[5] 5. McAuley, L. F., A note on collectionwise normality and paracompactness, Proc. Amer. Math. Soc. 9 (1958), 796–799. Google Scholar

[6] 6. Moore, R. L., Foundations of point set topology, Amer. Math. Soc. Col., Publ. XIII, New York, 1932. Google Scholar

[7] 7. Moran, W., Measures on metacompact spaces, Proc. London Math. Soc. III 20 (1970), 507–524. Google Scholar

[8] 8. Shirota, T., A class of topological spaces, Osaka J. Math. 4, (1952), 23–40. Google Scholar

Cité par Sources :