A characterization of equivariant absolute extensors and the equivariant Dugundji theorem

• Autores: Sergey A. Antonyan
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 2, 2005, págs. 451-462
• Idioma: inglés
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• Resumen

  • Let G be a compact Lie group. We prove that a metrizable G-space X is a G-ANE (resp., a G-AE) iff X is an ANE (resp., an AE) and, for any subgroup H of G which is the intersection of finitely many stabilizers in X, the H-fixed point set X[H] is a strong neighborhood H-deformation retract (resp., a strong H-deformation retract) of X. If a G-space X has no G-fixed point, then X is a G-ANE provided that X is an H-ANE for any subgroup H of G that occurs as a stabilizer in X. As an application, we give a new proof of the equivariant Dugundji extension theorem in the metrizable case.