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Mat. Sb., 1989, Volume 180, Number 8, Pages 1092–1118 (Mi msb1651)  

This article is cited in 50 scientific papers (total in 50 papers)

Topological groups and Dugundji compacta

V. V. Uspenskii


Abstract: A compact space $X$ is called a Dugundji compactum if for every compact $Y$ containing $X$, there exists a linear extension operator
$$\Lambda\colon C(X)\to C(Y),$$
which preserves nonnegativity and maps constants into constants. It is known that every compact group is a Dugundji compactum. In this paper we show that compacta connected in a natural way with topological groups enjoy the same property. For example, in each of the following cases, the compact space $X$ is a Dugundji compactum:
1) $X$ is a retract of an arbitrary topological group;
2) $X=\beta P$, where $P$ is a pseudocompact space on which some $\aleph_0$-bounded topological group acts transitively and continuously.
Bibliography: 57 titles.

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English version:
Mathematics of the USSR-Sbornik, 1990, 67:2, 555–580

Bibliographic databases:

UDC: 512.546
MSC: Primary 22C05, 54D30; Secondary 54B25, 54C15
Received: 16.06.1988

Citation: V. V. Uspenskii, “Topological groups and Dugundji compacta”, Mat. Sb., 180:8 (1989), 1092–1118; Math. USSR-Sb., 67:2 (1990), 555–580

Citation in format AMSBIB
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\paper Topological groups and Dugundji compacta
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 8
\pages 1092--1118
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\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 2
\pages 555--580
\crossref{https://doi.org/10.1070/SM1990v067n02ABEH002098}
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