Geodesic
A Method for Constructing Semilattices of $G$-Compactifications
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 916-925.

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

We suggest a method for constructing $G$-spaces $X$ such that the semilattice of $G$-compactifications of $X$ coincides with the disjoint union of two semilattices corresponding to partitions of $X$ into subspaces in which the maximal elements are identified. This method is applied to construct examples of $G$-Tychonoff spaces for which the semilattices of equivariant compactifications are of fairly simple structure and contain elements which are minimal but not least.
Keywords: semilattice of $G$-compactifications, Tychonoff space, $G$-Tychonoff space
Mots-clés : compact Haudorff space, group action, equipartition, semilattice of equipartititions. 
@article{MZM_2007_82_6_a11,
     author = {A. M. Sokolovskaya},
     title = {A {Method} for {Constructing} {Semilattices} of $G${-Compactifications}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {916--925},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a11/}
}
TY  - JOUR
AU  - A. M. Sokolovskaya
TI  - A Method for Constructing Semilattices of $G$-Compactifications
JO  - Matematičeskie zametki
PY  - 2007
SP  - 916
EP  - 925
VL  - 82
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a11/
LA  - ru
ID  - MZM_2007_82_6_a11
ER  - 
%0 Journal Article
%A A. M. Sokolovskaya
%T A Method for Constructing Semilattices of $G$-Compactifications
%J Matematičeskie zametki
%D 2007
%P 916-925
%V 82
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a11/
%G ru
%F MZM_2007_82_6_a11
A. M. Sokolovskaya. A Method for Constructing Semilattices of $G$-Compactifications. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 916-925. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a11/

[1] K. L. Kozlov, V. A. Chatyrko, “O bikompaktnykh $G$-rasshireniyakh”, Matem. zametki, 78:5 (2005), 695–709 | MR | Zbl

[2] J. M. Smirnov, L. N. Stojanov, “On minimal equivariant compact extensions”, C. R. Acad. Bulgare Sci., 36:6 (1983), 733–736 | MR | Zbl

[3] Yu. M. Smirnov, “Mogut li prostye geometricheskie ob'ekty byt maksimalnymi kompaktnymi rasshireniyami dlya $\mathbb R^n$”, UMN, 49:6 (1994), 213–214 | MR | Zbl

[4] Yu. M. Smirnov, “Minimalnye topologii na deistvuyuschikh gruppakh”, UMN, 50:6 (1995), 217–218 | MR | Zbl

[5] A. M. Sokolovskaya, “Suschestvovanie $G$-tikhonovskikh prostranstv, polureshetki bikompaktnykh $G$-rasshirenii kotorykh imeyut minimalnye ne naimenshie elementy”, Aleksandrovskie chteniya – 2006, Tezisy dokladov mezhdunarodnoi konferentsii, posvyaschennoi 110-letiyu so dnya rozhdeniya Pavla Sergeevicha Aleksandrova, M., 2006, 37–38

[6] J. de Vries, “On the existense of $G$-compactifications”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 26:3 (1978), 275–280 | MR | Zbl

[7] J. de Vries, Topological transformation groups I. A categorical approach, Mathematical Centre Tracts, 65, Mathematisch Centrum, Amsterdam, 1975 | MR | Zbl

[8] G. Birkgof, Teoriya reshetok, Nauka, M., 1984 | MR | Zbl

[9] A. G. Kurosh, Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[10] R. Engelking, Obschaya topologiya, Mir, M., 1986 | MR | Zbl