## A new construction of semi-free actions on Menger manifolds

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- by Sergei M. Ageev and Dušan Repovš PDF
- Proc. Amer. Math. Soc.
**129**(2001), 1551-1562 Request permission

## 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 $g\in G_{i}\setminus \{e \}$.## References

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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
**Dušan Repovš**- Affiliation: Institute for Mathematics, Physics and Mechanics, University of Ljubljana, 1001 Ljubljana, Slovenia
- MR Author ID: 147135
- ORCID: 0000-0002-6643-1271
- Email: dusan.repovs@fmf.uni-lj.si
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**129**(2001), 1551-1562 - MSC (1991): Primary 57S10, 54C55
- DOI: https://doi.org/10.1090/S0002-9939-00-05661-6
- MathSciNet review: 1712874