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JSYML
2010

Topological properties of sets definable in weakly o-minimal structures

9 years 5 months ago
Topological properties of sets definable in weakly o-minimal structures
The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [MMS] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large subsets of Cartesian products of definable sets, showing that if X, Y and S are non-empty definable sets and S is a large subset of X
Roman Wencel
Added 20 May 2011
Updated 20 May 2011
Type Journal
Year 2010
Where JSYML
Authors Roman Wencel
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