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Locally definable homotopy

Baro González, Elías and Otero, Margarita (2010) Locally definable homotopy. Annals of Pure and Applied Logic, 161 (4). pp. 488-503. ISSN 0168-0072

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Abstract

In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. (2009) 15pp, in press (doi:10.1093/qmath/hap011)] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in V-definable groups - which are examples of locally definable spaces. We show that the various concepts of connectedness associated to these groups, which have appeared in the literature, are non-equivalent.

Item Type:Article
Uncontrolled Keywords:O-minimality; Locally definable space; Locally definable group; Connectedness; O-minimal homotopy; Homotopy functor; Homology functor
Subjects:Sciences > Mathematics > Logic, Symbolic and mathematical
ID Code:14472
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Deposited On:30 Jan 2012 08:31
Last Modified:06 Feb 2014 10:02

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