Submission date: 9 December 2009.

Abstract:

In On o-minimal homotopy groups 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 equivalent.

Mathematics Subject Classification: 03C64, 14P10, 55Q99.

Keywords and phrases:

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