Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 111

Preprint Number 111

Previous Next Preprint server

111. Roman Wencel
Topological properties of sets definable in weakly o-minimal structures

Submission date: 4 January 2008.


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 weakly o-minimal structures. 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 of Macpherson, Marker and Steinhorn for sets and functions definable in models of weakly o-minimal theories. In the paper we also investigate large definable subsets of cartesian products of definable sets. Finally, we find various conditions equivalent to the fact that the topological dimension has the addition property.

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text: pdf, dvi, ps.

Last updated: January 8 2008 12:09 Please send your corrections to: