Geodesic
Shape Morphisms to Transitive $G$-Spaces
Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 821-827.

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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. 
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     author = {P. S. Gevorgyan},
     title = {Shape {Morphisms} to {Transitive} $G${-Spaces}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a3/}
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P. S. Gevorgyan. Shape Morphisms to Transitive $G$-Spaces. Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 821-827. http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a3/

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