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

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*, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR**0423357****[**T. A. Chapman,**CH**]*Dense sigma-compact subsets of infinite-dimensional manifolds*, Trans. Amer. Math. Soc.**154**(1971), 399–426. MR**0283828**, 10.1090/S0002-9947-1971-0283828-7**[**L. Montejano,**MO**]*Lusternik-Schnirelmann category and Hilbert cube manifolds*, Preprint.**[**Luis Montejano,**MO**]*A quick proof of Singhof’s 𝑐𝑎𝑡(𝑀×𝑆¹)=𝑐𝑎𝑡(𝑀)+1 theorem*, Manuscripta Math.**42**(1983), no. 1, 49–52. MR**693418**, 10.1007/BF01171745**[JA]**I. M. James,*On category, in the sense of Lusternik-Schnirelmann*, Topology**17**(1978), no. 4, 331–348. MR**516214**, 10.1016/0040-9383(78)90002-2**[WE]**James E. West,*Infinite products which are Hilbert cubes*, Trans. Amer. Math. Soc.**150**(1970), 1–25. MR**0266147**, 10.1090/S0002-9947-1970-0266147-3

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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