MÁRIO EDMUNDO

FACULDADE DE CIÊNCIAS, UNIVERSIDADE DE LISBOA

On definable normality

ABSTRACT :: :

Definably normal is the notion analogue to normal topological spaces for definable spaces in o-minimal structures. We will mention and prove a couple of lemmas about definable normality. These lemmas play a fundamental role in several places, via the shrinking lemma, e.g. in the theory of definable groups, ominimal cohomology and sheaves. In topology some of these lemmas are false but the definable analogues are true due to tameness of o-minimal structures and, the ones that are true in topology are trivial but their definable analogue require extra work and tools.

 

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