caa a22 4500 467979588 CHVBK 20180323112515.0 cr unu---uuuuu 170328e19900501xx s 000 0 eng 10.1007/BF02844766 doi (NATIONALLICENCE)springer-10.1007/BF02844766 Properties of countable separation and implicit function theorem [Elektronische Daten] [Cristina Di Bari, Pasquale Vetro] 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. Springer, 1990 Di Bari Cristina Dipartimento di Matematica ed Applicazioni, Via Archirafi, 34, 90123, Palermo aut Vetro Pasquale Dipartimento di Matematica ed Applicazioni, Via Archirafi, 34, 90123, Palermo aut Rendiconti del Circolo Matematico di Palermo Springer-Verlag 39/2(1990-05-01), 315-330 0009-725X 39:2<315 1990 39 12215 https://doi.org/10.1007/BF02844766 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02844766 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Di Bari Cristina Dipartimento di Matematica ed Applicazioni, Via Archirafi, 34, 90123, Palermo aut NATIONALLICENCE 700 1- Vetro Pasquale Dipartimento di Matematica ed Applicazioni, Via Archirafi, 34, 90123, Palermo aut NATIONALLICENCE 773 0- Rendiconti del Circolo Matematico di Palermo Springer-Verlag 39/2(1990-05-01), 315-330 0009-725X 39:2<315 1990 39 12215 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer