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

• Type: Journal
• Year: 2010
• Where: JSYML
• Authors: Roman Wencel
• Keywords: Definable Sets, JSYML 2010, Topological Dimension, Weakly O-minimal Structure