This article is cited in 14 papers

On $G$-Compactifications

K. L. Kozlov^a, V. A. Chatyrko<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Linköping University

Abstract: The semilattice of $G$-compactifications of a $G$-Tikhonov space $X$ is studied. The question of what sets containing $X$ and contained in the maximal $G$-compactification $\beta_GX$ must be contained also in all other $G$-compactifications of $X$ is considered. Conditions for $\beta_GX$ to be the completion of the $G$-space $X$ with respect to a natural uniformity (proximity) on $X$ are obtained. Sufficient conditions for the existence of a smallest (minimal, unique) $G$-compactification of $X$ are given.

UDC: 515.122.4+515.122.536

Received: 09.04.2004
Revised: 21.03.2005

DOI: 10.4213/mzm2629

 English version: Mathematical Notes, 2005, 78:5, 649–661

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