A Hilbert cube L-S category

Author:
Raymond Y. Wong

Journal:
Proc. Amer. Math. Soc. **102** (1988), 720-722

MSC:
Primary 57N20; Secondary 55M30, 58B05

DOI:
https://doi.org/10.1090/S0002-9939-1988-0929009-0

MathSciNet review:
929009

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Abstract: Let be a compact connected Hilbert cube manifold (-manifold). Define to be the smallest integer such that can be covered with open subsets each of which is homeomorphic to . Recently L. Montejano proved that, for every compact connected polyhedron , where is the Lusternik-Schnirelmann category of . Using a different approach, we prove a noncompact analog of the above theorem by showing that for every compact connected polyhedron .

**[**T. A. Chapman,**CH**]*Lectures on Hilbert cube manifolds*, CBMS Regional Conf. Ser. in Math., no. 28, Amer. Math. Soc., Providence, R. I., 1975. MR**0423357 (54:11336)****[**-,**CH**]*Dense sigma-compact subsets of infinite-dimensional manifolds*, Trans. Amer. Math. Soc.**154**(1971), 399-426. MR**0283828 (44:1058)****[**L. Montejano,**MO**]*Lusternik-Schnirelmann category and Hilbert cube manifolds*, Preprint.**[**-,**MO**]*A quick proof of Singhof's**theorem*, Manuscripta Math.**42**(1983), 49-52. MR**693418 (85a:55002)****[JA]**I. M. James,*On category, in the sense of Lusternik-Schnirelmann*, Topology**19**(1978), 331-349. MR**516214 (80i:55001)****[WE]**J. E. West,*Infinite products which are Hilbert cubes*, Trans. Amer. Math. Soc.**150**(1970), 1-25. MR**0266147 (42:1055)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0929009-0

Keywords:
Lusternik-Schnirelmann category,
Hilbert cube manifold,
polyhedron,
-sets

Article copyright:
© Copyright 1988
American Mathematical Society