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Mat. Zametki, 2002, Volume 72, Issue 6, Pages 821–827 (Mi mz469)  

This article is cited in 1 scientific paper (total in 1 paper)

Shape Morphisms to Transitive $G$-Spaces

P. S. Gevorgyan

M. V. Lomonosov Moscow State University

Abstract: The following problem plays an important role in shape theory: find conditions that guarantee that a shape morphism $F\colon X\mapsto Y$ of a topological space $X$ to a topological space $Y$ is generated by a continuous mapping $f\colon X\mapsto Y$. In the present paper, we study this problem in equivariant shape theory and give a solution for shape-equivariant morphisms to transitive $G$-spaces, where $G$ is a compact group with countable base. As a corollary, we prove a sufficient condition for equivariant shapes of a $G$-space $X$ to be equal to the group $G$ itself. We also prove some statements concerning equivariant bundles that play the key role in the proof of the main results and are of interest on their own.

DOI: https://doi.org/10.4213/mzm469

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English version:
Mathematical Notes, 2002, 72:6, 757–762

Bibliographic databases:

UDC: 515.122.6
Received: 23.07.2001

Citation: P. S. Gevorgyan, “Shape Morphisms to Transitive $G$-Spaces”, Mat. Zametki, 72:6 (2002), 821–827; Math. Notes, 72:6 (2002), 757–762

Citation in format AMSBIB
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\by P.~S.~Gevorgyan
\paper Shape Morphisms to Transitive $G$-Spaces
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 6
\pages 821--827
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\jour Math. Notes
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\pages 757--762
\crossref{https://doi.org/10.1023/A:1021429627291}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Derikvand T. Kamyabi-Gol R.A. Janfada M., “Isometric Isomorphism of Homogeneous Space Algebras”, Publ. Math.-Debr., 93:1-2 (2018), 125–142  crossref  isi
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