# Fixed point sets of transformation groups of Menger manifolds, their pseudo-interiors and their pseudo-boundaries

```@article{Iwamoto1996FixedPS,
title={Fixed point sets of transformation groups of Menger manifolds, their pseudo-interiors and their pseudo-boundaries},
author={Yutaka Iwamoto},
journal={Topology and its Applications},
year={1996},
volume={68},
pages={267-283}
}```
Abstract Let G be a compact separable zero-dimensional group with the unit element e . We construct semifree G -actions on Menger manifolds with G -invariant pseudo-interiors and pseudo-boundaries. The main purpose of this paper is to prove the following: For each closed subset X of a Menger manifold M, there exists a semifree G-action on M such that X is the fixed point set of any g ϵ G ⧹ { e }. This gives the affirmative answers to the questions in K. Sakai, Preprint and in A. Chigogidze, K… Expand
8 Citations
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PII: S0166-8641(98)00124-2
This is an updated survey on Menger manifold theory after the publication of “Menger manifolds” by Chigogidze et al. inContinua with Houston Problem Book (Marcel Dekker, 1995). 2000 Elsevier ScienceExpand

#### References

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Let μn be the n-dimensional universal Menger compactum, X a Z-set in μn and G a metrizable zero-dimensional compact group with e the unit. It is proved that there exists a semi-free G-action on μnExpand
ON FREE ACTIONS OF ZERO-DIMENSIONAL COMPACT GROUPS
It is proved that there exists a free action of an arbitrary zero-dimensional compact group on every Menger manifold. It is shown that in the case of a finite group G such a G-action on theExpand
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• Mathematics
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Abstract For each k ⩾ 1, we introduce the categorical and the geometric pseudo-interiors of the k -dimensional universal Menger compacta and prove that they are homeomorphic to the universal NobelingExpand
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