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Semi-free actions of zero-dimensional compact groups on Menger compacta

Authors:	Katsuro Sakai

Institution:	Institute of Mathematics, University of Tsukuba, Tsukuba-city 305, Japan

Abstract:	Let $\mu ^{n}$ be the -dimensional universal Menger compactum, a -set in $\mu ^{n}$ and a metrizable zero-dimensional compact group with the unit. It is proved that there exists a semi-free -action on $\mu ^{n}$ such that is the fixed point set of every $g \in G \smallsetminus \{e\}$ . As a corollary, it follows that each compactum with $\dim \leqslant n$ can be embedded in $\mu ^{n}$ as the fixed point set of some semi-free -action on $\mu ^{n}$ .

Keywords:	The fixed point set semi-free action $0$-dimensional compact group the $n$-dimensional universal Menger compactum

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