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A Note on the Category of the Telescope
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1977
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