Por Mário Edmundo (Faculdade de Ciências, CMAF-CIO, Universidade de Lisboa).

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, o-minimal 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.