Massabò, Ivar; Vignoli, Alfonso On the théorème fondamental of J. Leray and J. Schauder. (English) Zbl 0698.47049 Colloq. Math. 57, No. 2, 265-272 (1989). The classical “théorème fondamental” of J. Leray and J. Schauder states, loosely speaking, that the fixed ponts of one-parameter families of compact maps (“admissible homotopies”) are conserved over the whole parameter interval [0,1]. Some essential generalizations are discussed in this interesting note. A basic tool is the notion of “0-epi maps” introduced by M. Furi, M. Martelli and the second author in Ann. Mat. Pura Appl. 124, 321-343 (1980; Zbl 0456.47051). Reviewer: J.Appell MSC: 47J05 Equations involving nonlinear operators (general) 55M25 Degree, winding number Keywords:Leray-Schauder degree; fixed ponts of one-parameter families of compact maps; admissible homotopies; 0-epi maps Citations:Zbl 0456.47051 PDFBibTeX XMLCite \textit{I. Massabò} and \textit{A. Vignoli}, Colloq. Math. 57, No. 2, 265--272 (1989; Zbl 0698.47049) Full Text: DOI