Geodesic
On Wallman compactifications of $T_0$-spaces and related questions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 102-111 
L. I. Calmuţchi; M. M. Choban. On Wallman compactifications of $T_0$-spaces and related questions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 102-111. http://geodesic.mathdoc.fr/item/BASM_2011_2_a8/
@article{BASM_2011_2_a8,
     author = {L. I. Calmu\c{t}chi and M. M. Choban},
     title = {On {Wallman} compactifications of $T_0$-spaces and related questions},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {102--111},
     year = {2011},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2011_2_a8/}
}
TY  - JOUR
AU  - L. I. Calmuţchi
AU  - M. M. Choban
TI  - On Wallman compactifications of $T_0$-spaces and related questions
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2011
SP  - 102
EP  - 111
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/BASM_2011_2_a8/
LA  - en
ID  - BASM_2011_2_a8
ER  - 
%0 Journal Article
%A L. I. Calmuţchi
%A M. M. Choban
%T On Wallman compactifications of $T_0$-spaces and related questions
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2011
%P 102-111
%N 2
%U http://geodesic.mathdoc.fr/item/BASM_2011_2_a8/
%G en
%F BASM_2011_2_a8

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

We study the compactification of the Wallman–Shanin type of $T_0$-spaces. We have introduced the notion of compressed compactification and proved that any compressed compactification is of the Wallman–Shanin type. The problem of the validity of the equality $\omega(X\times Y)=\omega X\times\omega Y$ is examined. Two open questions have arisen.

[1] Alo R. A., Shapiro H. L., “Wallman compact and realcompact spaces”, Contribs. Extens. Theory Topol. Struct., Proceed. Sympos. (Berlin, 1967), Berlin, 1969, 9–14 | MR | Zbl

[2] Arhangel'skii A. V., “A study of remainders of topological groups”, Fund. Math., 203 (2009), 165–178 | DOI | MR | Zbl

[3] Arhangel'skii A. V., Choban M. M., “Remainders of rectifiable spaces”, Topology and Appl., 157 (2010), 789–799 | DOI | MR | Zbl

[4] Arhangel'skii A. V., Choban M. M., “Some addition theorems for rectifiable spaces”, Buletinul Acad. de Ştiinţe a Rep. Moldova, Matematica, 2011, no. 2(66), 60–69 | MR | Zbl

[5] Choban M. M., Calmuţchi L. I., “Some problems of the theory of compactifications of topological spaces”, ROMAI Journal, 2:1 (2006), 25–51 | MR | Zbl

[6] Engelking E., General Topology, PWN, Warszava, 1977 | Zbl

[7] Faulkner G. D., Vipera M. C., “Remainders of compactifications and their relation to a quotient lattice of the topology”, Proc. Amer. Math. Soc., 122 (1994), 931–942 | DOI | MR | Zbl

[8] Frink O., “Compactifications and semi-normal spaces”, Amer. J. Math., 86 (1964), 602–607 | DOI | MR | Zbl

[9] Gillman L., Jerison M., Rings of continuous functions, Springer-Verlag, New York, 1976 | MR | Zbl

[10] Shanin N. A., “On special extension of topological spaces”, Dokl. AN SSSR, 38 (1943), 7–11 (in Russian) | MR

[11] Dokl. AN SSSR, 217 (1974), 38–41 | MR | Zbl

[12] Steiner E. F., “Wallman spaces and compactifications”, Fund. Math., 61 (1968), 295–304 | MR | Zbl

[13] Dokl. AN SSSR, 233 (1977), 1056–1059 | MR

[14] Wajch E., “Complete rings of functions and Wallman-Frink compactifications”, Colloq. Math., 56:2 (1988), 281–290 | MR | Zbl