On a theorem of Jaworowski on locally equivariant contractible spaces

Authors:
Sergei M. Ageev and Dusan Repovs

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1539-1550

MSC (1991):
Primary 54C55, 57S10; Secondary 54C20, 54C60, 54F65, 55M15

DOI:
https://doi.org/10.1090/S0002-9939-01-06184-6

Published electronically:
October 5, 2001

MathSciNet review:
1879981

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Ancel's method of fiberwise trivial relations is applied to the problem of characterization of absolute equivariant extensors. We obtain a generalization of Jaworowski's theorem on characterization of equivariant extensors lying in to the case when the space is infinite-dimensional, has infinitely many orbit types and the acting compact group is not necessarily a Lie group.

**[Ab]**H. Abels,*A universal proper**-space*, Math. Z.**159**(1978), 143-158. MR**58:18504****[AG]**D. F. Addis and J. H. Gresham,*A class of infinite-dimensional spaces I, Dimension theory and Aleksandroff's problem*, Fund. Math.**101**(1978), 195-205. MR**80b:54041****[Ag]**S. M. Ageev,*An equivariant Dugundji theorem*, Uspehi Mat. Nauk**45**:5 (1990), 116-117 (in Russian); Engl. transl. in: Russ. Math. Surv.**45**:5 (1990), 219-220. MR**92h:54026****[An]**F. D. Ancel,*The role of countable dimensionality in the theory of cell-like relations*, Trans. Amer. Math. Soc.**287**(1985), 1-40. MR**86b:54012****[Bo]**K. Borsuk,*Theory of Retracts*, Monogr. Matem.**44**, PWN, Warsaw, 1967. MR**35:7306****[Br]**G. E. Bredon,*Introduction to Compact Transformation Groups*, Pure and Appl. Math.**46**, Academic Press, New York-London, 1972. MR**54:1265****[Ca]**R. Cauty,*Un espace metrique lineaire qui n'est pas un retracte absolu*, Fund. Math.**146**(1994), 85-99. MR**95j:54022****[Do]**C. H. Dowker,*Homotopy extension theorems*, Proc. London Math. Soc.**6**(1956), 100-116. MR**17:518f****[Ha]**W. E. Haver,*Locally contractible spaces that are absolute neighborhood retracts*, Proc. Amer. Math. Soc.**40**(1973), 280-284. MR**48:9645****[Hu]**S.-T. Hu,*Theory of Retracts*, Wayne State Univ. Press, Detroit, 1965. MR**31:6202****[Ja]**J. Jaworowski,*Extensions of**-maps and Euclidean**-retracts*, Math. Z.**146**(1976), 143-148. MR**52:15351****[Ma]**S. Mardesic,*Approximate polyhedra, resolutions of maps and shape fibrations*, Fund. Math.**114**(1981), 53-78. MR**83d:55016****[Mx]**C. N. Maxwell,*Homeomorphisms of topological transformation groups into function spaces*, Duke Math. J.**33**(1966), 567-574. MR**34:3563****[Mu]**T. Murayama,*On**-**'s and their**-homotopy types*, Osaka J. Math.**20**(1983), 479-512. MR**85f:57022****[Pa]**R. S. Palais,*The classification of**-spaces*, Memoirs Amer. Math. Soc.**36**(1960). MR**31:1664****[RS]**D. Repovs and P. V. Semenov,*Continuous Selections of Multivalued Mappings*, Mathematics and Its Appl.**455**, Kluwer, Dordrecht, 1998. MR**2000a:54002****[To]**H. Torunczyk,*Concerning locally homotopy negligible sets and characterization of**-manifolds*, Fund. Math.**101**(1978), 93-110. MR**80g:57019****[Vi]**G. Villalobos,*Inversion of the theorem on the existence of slices*, Vestnik MSU (1) (2000), 26-29 (in Russian).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
54C55,
57S10,
54C20,
54C60,
54F65,
55M15

Retrieve articles in all journals with MSC (1991): 54C55, 57S10, 54C20, 54C60, 54F65, 55M15

Additional Information

**Sergei M. Ageev**

Affiliation:
Department of Mathematics, Brest State University, Brest, Belarus 224011

Email:
ageev@highmath.brsu.brest.by

**Dusan Repovs**

Affiliation:
Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001

Email:
dusan.repovs@uni-lj.si

DOI:
https://doi.org/10.1090/S0002-9939-01-06184-6

Keywords:
Local equivariant contractibility,
absolute equivariant extensor,
fiberwise trivial relation,
countable dimensional orbit space,
selections of multivalued maps

Received by editor(s):
May 17, 2000

Received by editor(s) in revised form:
November 10, 2000

Published electronically:
October 5, 2001

Communicated by:
Alan Dow

Article copyright:
© Copyright 2001
American Mathematical Society