Maia Dzadzamia


The shape theory of continuous maps is a new branch of classical shape theory and is an extension of the homotopy theory of absolute neighborhood retracts for the category of maps of metrizable spaces. In this paper we investigate theory of absolute equivariant (neighborhood) retracts and extensors for maps of topological G-spaces from a weakly hereditary class.


G-map; equivariant retraqt; equivariant extensor; equivariant absolut (neighborhood) retracts and extensors for G-maps

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Antonian, S. A. (1987). Equivariant embeddings into G-AR’s, Glas. Mat. 22 (42), P. 503-533.

Antonian, S. A. & Mardešic, S. (1987). Equivariant shape. Fund. Math., 127, P. 213–224.

Baladze, V. (1988). On shape theory for fibrations, Bull. Georgian Acad. Sci., 129, P. 269-272.

Baladze, V. (1991). Fiber shape theory and resolutions, Zb. Rad. Filoz. Fak. Nisu, Ser. Mat. 5, P. 97-107.

Baladze, V. (2003). Fiber shape theory, Proc. A. Razmadze Math. Inst., 132, P. 1-70.

Baladze, V. & Dzadzamia, M. (2002). On retracts of compact transformation groups. Bull. Georgian Acad. Sci. 166, No 2, 217-221.

Dold, A. (1974). The fixed index of fibr-preserving maps. Invent. Math., 25, P. 281-298.

Gevorgyan, P. S. (2001). Generalized shape theory and movability of continuous transformation groups, Dissertation, MSU

Nepomniachy, G. M. & Smirnov, Yu. M. (1979). On retraction of mappings. (Russian) Chechoslovak math. J.104, No.29, P. 366-377.

Ungar, G. S. (1977). ANR’s and NES ’s in the category of mapping of matric spaces. Fund. Math. 95, P. 111-127.


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