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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new construction of semi-free actions on Menger manifolds


Authors: Sergei M. Ageev and Dusan Repovs
Journal: Proc. Amer. Math. Soc. 129 (2001), 1551-1562
MSC (1991): Primary 57S10, 54C55
Published electronically: October 24, 2000
MathSciNet review: 1712874
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Abstract:

A new construction of semi-free actions on Menger manifolds is presented. As an application we prove a theorem about simultaneous coexistence of countably many semi-free actions of compact metric zero-dimensional groups with the prescribed fixed-point sets: Let $G$ be a compact metric zero-dimensional group, represented as the direct product of subgroups $G_{i}$, $M$ a $\mu ^{n}$-manifold and $\nu (M)$(resp., $\Sigma (M)$) its pseudo-interior (resp., pseudo-boundary). Then, given closed subsets $X_{i}, i\ge 1,$ of $M$, there exists a $G$-action on $M$ such that (1) $\nu (M)$ and $\Sigma (M) $ are invariant subsets of $M$; and (2) each $X_{i}$ is the fixed point set of any element $g\in G_{i}\setminus \{e \}$.


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Additional Information

Sergei M. Ageev
Affiliation: Department of Mathematics, Brest State University, 224011 Brest, Belarus
Email: ageev@highmath.brsu.brest.by

Dusan Repovs
Affiliation: Institute for Mathematics, Physics and Mechanics, University of Ljubljana, 1001 Ljubljana, Slovenia
Email: dusan.repovs@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05661-6
PII: S 0002-9939(00)05661-6
Keywords: Semi-free action, Menger manifold, absolute extensor in finite dimension
Received by editor(s): May 22, 1998
Received by editor(s) in revised form: August 12, 1999
Published electronically: October 24, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society