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A Note on the Category of the Telescope

Published online by Cambridge University Press:  20 November 2018

K. A. Hardie
K. A. Hardie*
Affiliation:
Department of MathematicsUniversity of Capetown Rondebosch7700, Republic of South Africa
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Let X be an infinite connected CW-complex which is the union of an increasing sequence of subcomplexes Xr. Let cat X denote the Lusternik-Schnirelmann category of X, normalized to take the value 0 on contractible spaces. Suppose that cat Xr ≤ K (r ≥ 1). In his problem list [1], T. Ganea proved that cat Xr ≤ 2k +1 and asked (Problem 5) whether this is the best possible upper bound. The purpose of this note is to prove that cat X ≤ 2k.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 107
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Ganea, T., Some problems on numerical homotopy invariants. Symposium on Algebraic Topology, Battelle Seattle Research Centre 1971, Lecture Notes in Mathematics 249, Springer-Verlag, Berlin, 1971.Google Scholar
2. Hardie, K. A., On the category of the double mapping cylinder, Töhoku Mathematical Journal, 25 (1973), 355-358.Google Scholar