Some classical analysis results for continuous definable mappings (Q2154421)

The authors show that some fundamental results for smooth mappings in global analysis have natural extensions for continuous mappings that are definable in o-minimal structures (for definition and basic properties about this notion we refer to the book of [\textit{L. van den Dries}, Tame topology and o-minimal structures. Cambridge: Cambridge University Press (1998; Zbl 0953.03045)]). The paper is organized into six sections dealing with the following aspects: Introduction; Preliminaries (notation, o-minimal structures and definable mappings); Regular points and values of continuous definable mappings; The mean value theorem, the inverse function theorem and the implicit function theorem for continuous definable mappings; A formula for the Brouwer degree of continuous definable mappings; Global properties of continuous definable mappings.