Real Algebraic and Analytic Geometry
Submission: 2008, October 28.
This article gives a version of the homotopy theory (developed by H. Delfs and M. Knebusch in the semialgebraic case) extended to regular paracompact locally definable spaces and definable CW-complexes over a model $R$ of an o-minimal (complete) theory $T$ extending RCF, and even for weakly definable spaces, if $T$ is a bounded theory. Corresponding generalized homology and cohomology theories for pointed weak polytopes coincide with the known topological generalized theories if $T$ is bounded.
Mathematics Subject Classification (2000): 03C64, 55N20, 55Q05.
Keywords and Phrases: o-minimal structure, generalized topology, locally definable space, weakly definable space, CW-complex, homotopy sets, generalized homology, generalized cohomology.
Full text, 17p.: dvi 81k, ps.gz 349k, pdf 495k.