Journal of Mathematical Sciences

, Volume 186, Issue 6, pp 866–881 | Cite as

Retracts and extensors of compact transformation groups

  • M. Dzadzamia


In this paper, we study G-spaces, i.e., topological spaces with actions of a compact group G, from the point of view of the theory of retracts. We recall definitions and properties of absolute retracts, absolute neighborhood retracts, absolute extensors, and absolute neighborhood extensors with respect to the equivariant weakly hereditary class \( \mathfrak{G} \) of G-spaces. Also, we give basic notions of the theory of topological transformation groups.


Equivariant Mapping Invariant Subset Equivariant Retraction Absolute Retract Bredon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Antonian, “Equivariant embeddings into G-ARs,” Glas. Mat. Ser. III, 22 (42), No. 2, 503–533 (1987).MathSciNetGoogle Scholar
  2. 2.
    S. A. Antonian and S. Mardešić, “Equivariant shapes,” Fund. Math., 127, No. 3, 213–224 (1987).MathSciNetMATHGoogle Scholar
  3. 3.
    K. Borsuk, Theory of Retracts, Panstwowe Wydawnictwo Naukowe, Warsaw (1967).Google Scholar
  4. 4.
    G. E. Bredon, “Equivariant cohomology theories,” Bull. Am. Math. Soc., 73, 266–268 (1967).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    G. E. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York–London, 1972.MATHGoogle Scholar
  6. 6.
    R. Engelking, General Topology, Polish Scientific Publishers, Warsaw (1977).MATHGoogle Scholar
  7. 7.
    Hu S.-Tsen, Theory of Retracts, Wayne State University Press, Detroit, 1965.MATHGoogle Scholar
  8. 8.
    Yu. M. Smirnov, “Shape theory for G-pairs,” Usp. Mat. Nauk, 40, No. 2 (242), 151–165 (1985).Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.S.Rustaveli Batumi State UniversityBatumiGeorgia

Personalised recommendations