A Hilbert cube L-S category
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- by Raymond Y. Wong PDF
- Proc. Amer. Math. Soc. 102 (1988), 720-722 Request permission
Abstract:
Let $M$ be a compact connected Hilbert cube manifold ($Q$-manifold). Define ${C_z}\left ( M \right )$ to be the smallest integer $k$ such that $M$ can be covered with $k$ open subsets each of which is homeomorphic to $Q \times \left [ {0,1} \right )$. Recently L. Montejano proved that, for every compact connected polyhedron $P,{C_z}\left ( {P \times Q} \right ) = \operatorname {cat}\left ( P \right ) + 1$, where $\operatorname {cat} \left ( P \right )$ is the Lusternik-Schnirelmann category of $P$. Using a different approach, we prove a noncompact analog of the above theorem by showing that ${C_z}\left ( {P \times Q \times \left [ {0,1} \right )} \right ) = \operatorname {cat}\left ( P \right )$ for every compact connected polyhedron $P$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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