Geodesic
A Note on the Category of the Telescope
Canadian mathematical bulletin, Tome 20 (1977) no. 1, p. 107

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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. 
Hardie, K. A. A Note on the Category of the Telescope. Canadian mathematical bulletin, Tome 20 (1977) no. 1, p. 107. doi: 10.4153/CMB-1977-018-4
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     title = {A {Note} on the {Category} of the {Telescope}},
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