Geodesic
Extension of the pseudo-compact group actions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 931-934

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It is proved that for a given pseudo-compact Hausdorff group $G$, every continuous action $\alpha\colon\,G\times X\to X$ on a metrizable space $X$ has a unique extension to a continuous action $\tilde{\alpha}\colon\,\beta G\times X\to X$, where $\beta G$ is the Stone–Cech extension of $G$. 
@article{FPM_2001_7_3_a21,
     author = {S. A. Antonyan},
     title = {Extension of the pseudo-compact group actions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {931--934},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a21/}
}
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S. A. Antonyan. Extension of the pseudo-compact group actions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 931-934. http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a21/