Real Algebraic and Analytic Geometry |

O-minimal homotopy and generalized (co)homology.

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homepage: http://www.cyf-kr.edu.pl/~pupiekos/

Submission: 2008, October 28.

*Abstract:
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.

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