This article is cited in 21 papers

Topological transformation groups and Dugundji compacta

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 presence of an algebraic structure on a space, which is compatible with its topology, in many cases imposes very strong restrictions on the properties of the space itself. Conditions are found which must be satisfied by the actions in order for the phase space to be a $d$-space (Dugundji compactum). This investigation allows the range of $G$-spaces that are $d$-spaces (Dugundji compacta) to be substantially widened. It is shown that all the cases known to the authors where a $G$-space (a topological group, one of its quotient spaces) is a $d$-space can be realized using equivariant maps.
Bibliography: 39 titles.

Keywords: $G$-space, topological group, Dugundji compactum, $d$-space, uniform structure.

UDC: 515.122.4+515.122.536

MSC: Primary 54H15; Secondary 22A05, 54B15, 54D30, 54D35, 54E15

Received: 26.06.2008 and 03.07.2009

DOI: 10.4213/sm6387

 English version: Sbornik: Mathematics, 2010, 201:1, 103–128

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