On the théorème fondamental of J. Leray and J. Schauder. (English) Zbl 0698.47049
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