Properties of countable separation and implicit function theorem
We consider some properties of countable separation for familiesA andD of subsets of a setX by means of elements of a fixed familyM⊂P(X). We give necessary and sufficient conditions, in terms of measurability of some sets constructed by means of multifunctions, in order that the familiesA andD satisfy such a property. As an application we derive an implicit function theorem for functions ofCarathéodory-type.
KeywordsTopological Space Measurable Space Closed Subset Implicit Function Theorem Countable Family
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- Averna D.,Separation properties in X and 2X:measurable multifunctions and graphs, Mat. Cas. (to appear).Google Scholar
- Cristensen J. P. R.,Topology and Borel structure, North-Holland Amsterdam, 1974.Google Scholar
- Di Bari C. M.,Measurability and countable separation, Rend. Circ. Mat. Palermo39 (1990).Google Scholar