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 β G X must be contained also in all other G-compactifications of X is considered. Conditions for β G X 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.
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Translated from Matematicheskie Zametki, vol. 78, no. 5, 2005, pp. 695–709.
Original Russian Text Copyright ©2005 by K. L. Kozlov, V. A. Chatyrko.
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Kozlov, K.L., Chatyrko, V.A. On G-Compactifications. Math Notes 78, 649–661 (2005). https://doi.org/10.1007/s11006-005-0168-y
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DOI: https://doi.org/10.1007/s11006-005-0168-y