Geodesic
Q-compactifications of metric spaces
Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 85-94 
A. V. Arkhangel'skii. Q-compactifications of metric spaces. Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 85-94. http://geodesic.mathdoc.fr/item/SM_1973_20_1_a4/
@article{SM_1973_20_1_a4,
     author = {A. V. Arkhangel'skii},
     title = {Q-compactifications of metric spaces},
     journal = {Sbornik. Mathematics},
     pages = {85--94},
     year = {1973},
     volume = {20},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_20_1_a4/}
}
TY  - JOUR
AU  - A. V. Arkhangel'skii
TI  - Q-compactifications of metric spaces
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 85
EP  - 94
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1973_20_1_a4/
LA  - en
ID  - SM_1973_20_1_a4
ER  - 
%0 Journal Article
%A A. V. Arkhangel'skii
%T Q-compactifications of metric spaces
%J Sbornik. Mathematics
%D 1973
%P 85-94
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1973_20_1_a4/
%G en
%F SM_1973_20_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

For $Q$-spaces (also called functionally closed or Hunt spaces) there are defined in this paper two new invariants, the $q$-weight and the $q^*$-weight. With the aid of these the following results are obtained. Theorem 1. {\it If $\tau$ is a nonmeasurable cardinal number and $X$ is a metric space of weight not exceeding $\tau$, then $X$ is homeomorphic to a closed subspace of the product of $\tau^{\aleph_0}$ copies of a real line $R$ $($i.e. X\subset_\mathrm{cl}R^{(\tau^{\aleph_0})})$}. \smallskip Theorem~2. {\it If~$\tau$ is a~nonmeasurable cardinal number and~$X$ is a~complete uniform space whose uniform and topological weights do not exceed~$\tau$, then~$X$ is homeomorphic to a~closed subspace of the product of $\tau^{\aleph_0}$ copies of the real line.} \smallskip Theorem~3. {\it Let~$X$ be paracompact, $bX$~a~Hausdorff compactification of~$X$, and~$\tau$ a~nonmeasurable cardinal number such that the weight of~$X$ does not exceed~$\tau$ and~$X$ is the intersection of a~family of not more than~$\tau$ open subsets of~$bX$. Then~$X$ is homeomorphic to a~closed subspace of the product of $\tau^{\aleph_0}$ copies of the real line.} Bibliography: 8 titles.

[1] A. V. Arkhangelskii, “O bikompaktakh, udovletvoryayuschikh usloviyu Suslina nasledstvenno. Tesnota i svobodnye posledovatelnosti”, DAN SSSR, 199:6 (1971), 1227–1230

[2] L. Gillman, M. Jerison, Rings of continuous functions, van Nostrand, New York, 1960 | MR | Zbl

[3] H. J. Kowalsky, “Einbettung metrischen Räume”, Arch. Math., 8 (1957), 336–339 | DOI | MR | Zbl

[4] R. Engelking, Outline of General Topology, Amsterdam, 1968 | MR

[5] Dzh. L. Kelli, Obschaya topologiya, izd-vo «Nauka», Moskva, 1968

[6] J. van der Slot, Universal topological properties, ZW 1966-011, Amsterdam, 1966, 1–9 | MR

[7] Jun-iti Nagata, Modern General Topology, Amsterdam, 1968 | MR

[8] A. V. Arkhangelskii, “Ob odnom klasse prostranstv, soderzhaschem vse metricheskie i vse lokalno bikompaktnye prostranstva”, Matem. sb., 67 (109) (1965), 55–85