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Function spaces of CW homotopy type are Hilbert manifolds
Author(s):
Jaka
Smrekar;
Atsushi
Yamashita
Journal:
Proc. Amer. Math. Soc.
137
(2009),
751-759.
MSC (2000):
Primary 54C35;
Secondary 55M15, 57N20
Posted:
August 28, 2008
MathSciNet review:
2448598
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Abstract:
Let  be a countable CW complex and  an ANR (for metric spaces) and let  denote the space of continuous maps from  to  with the compact-open topology. We show that, under mild restrictions, the following are equivalent: (1)  is an  -manifold, (2)  is an ANR, (3)  has the homotopy type of a CW complex. We also give a few interesting examples and applications.
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Additional Information:
Jaka
Smrekar
Affiliation:
Fakulteta za Matematiko in Fiziko, Jadranska ul. 19, SI-1111 Ljubljana, Slovenia
Email:
jaka.smrekar@fmf.uni-lj.si
Atsushi
Yamashita
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email:
yonster@ms.u-tokyo.ac.jp
DOI:
10.1090/S0002-9939-08-09584-1
PII:
S 0002-9939(08)09584-1
Received by editor(s):
February 1, 2008
Posted:
August 28, 2008
Additional Notes:
The first author was supported in part by the ARRS research project No. J1-6128-0101-04.
The second author was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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