Union of equivariant extensors and equivariant covering spaces

• Autorzy: Jimenez, R. , Neymet, S.
• Języki publikacji: EN

Abstrakty

EN

Let G be a compact topological group and P be the class of all paracompact and Hausdorff G-spaces. We prove that a paracompact space that is a local G-AN E(P) is a G-AN E(P). Then we give an application to the theory of equivariant overlays by proving the following: Let p : [...] --> X be G-overlays of a metrizable connected G-space X. Then an equivariant map f : Z --> X from Z, a metrizable connected G-space, can be lifted to an equivariant map F : Z --> [...] if and only if f[...].

Słowa kluczowe

PL

G-przestrzeń nakrywająca; G-warstwa nałożona; topologia

EN

G-AN R; G-covering spaces; G-overlays; local G-AN R; orbit space

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 4
• Strony: 347--356
• Opis fizyczny: Bibliogr. s. 11 poz.

Twórcy

autor

Jimenez, R.

• Instituto de matematicas, Unam, AV, Universidad S/N Col., Lomas de Chamilpa, 62210 Cuernavaga, Morelos, Mexico,

autor

Neymet, S.

• Facultad de Ciencias, Unam, Circuioto Exterior, C.U, 04510 Mexico, D. F. Mexico,

Bibliografia

• [1] S. A. Antonian, S. Mardešić, Equivariant shape, Fund. Math., 127 (1987) 213-234.
• [2] S. A. Antonian, R. Jiménez, S. de Neymet, Fibrewise retraction and shape properties of the orbit space, Glas. Mat., to be published.
• [3] S. de Neymet, R. Jiménez, G-overlays, Bolyai Soc. Math. Stud., 4 (1993) 379-387.
• [4] R. Engelking, General topology, Heldermann Verlag-Berlin, 1989.
• [5] 0. Hanner, Retraction and extension of mapping of metric and non-metric spaces, Ark. Mat., 2 (1952) 315-360.
• [6] S. T. Hu, Theory of retracts, Wayne State Univ. Press, 1965.
• [7] S. Mardešić, J. Segal, Shape theory, North-Holland, 1982.
• [8] P. Mrozik, Images and exactness in the category of pro-groups and the lifting problem for covering projections, Glas. Mat., 28 (48) (1993) 209-226.
• [9] M. Murayama, On G-AN Rs and their G-homotopy types, Osaka J. Math., 20 (1983) 479-512.
• [10] R. Palais, The clasification of G-spaces, Mem. Amer. Math. Soc., 36 (1960).
• [11] Yu. M. Smirnov, Shape theory for G-pairs, Russian Math. Surveys, 40:2 (1985) 185-203.