2008/12/11 by Elías Baro, Elias Baro, Baro, Elias +2
Mathematics · #03C64 #14P10 #55Q99 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03C64 #msc:14P10 #msc:55Q99
paper · pdf · doi:10.48550/arxiv.0812.2112
arxiv created 2008/12/11 · openalex publication_date 2008/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 non-equivalent.