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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2002_72_6_a3,
     author = {P. S. Gevorgyan},
     title = {Shape {Morphisms} to {Transitive} $G${-Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {821--827},
     publisher = {mathdoc},
     volume = {72},
     number = {6},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a3/}
}
TY  - JOUR
AU  - P. S. Gevorgyan
TI  - Shape Morphisms to Transitive $G$-Spaces
JO  - Matematičeskie zametki
PY  - 2002
SP  - 821
EP  - 827
VL  - 72
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a3/
LA  - ru
ID  - MZM_2002_72_6_a3
ER  - 
%0 Journal Article
%A P. S. Gevorgyan
%T Shape Morphisms to Transitive $G$-Spaces
%J Matematičeskie zametki
%D 2002
%P 821-827
%V 72
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a3/
%G ru
%F MZM_2002_72_6_a3
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/