Locally definable homotopy

Annals of Pure and Applied Logic 161 (4):488-503 (2010)
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Abstract

In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] 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 -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

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References found in this work

Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
A semi-linear group which is not affine.Pantelis E. Eleftheriou - 2008 - Annals of Pure and Applied Logic 156 (2):287-289.

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