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Topological Localization, Category and Cocategory

Published online by Cambridge University Press:  20 November 2018

Graham Hilton Toomer
Graham Hilton Toomer*
Affiliation:
Cornell University, Ithaca, New York; Ohio State University, Columbus, Ohio
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It is easy to see that a localization (in the sense of [9]) of a simply connected co H-space (equivalently a simply connected space of Liusternik-Schnirelman category one) is again a co H-space. (All spaces in this paper will be pointed and have the based homotopy type of a connected CW complex; and all maps will preserve base-points.) We show that the category of a simply connected space does not increase on localizing. We give an example to show that the hypothesis simple-connectivity is crucial. In strong contrast, the dual result only requires connectivity.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 319 - 322
Copyright
Copyright © Canadian Mathematical Society 1975

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