An index theory for countably \(P\)-concentrative \(J\) maps
This article deals with a modification of Andres-Gabor-Gorniewicz' index theory of compact maps \(T\) in Fréchet space, \(T \in J(\overline{U},C)\) or, in other words, \(T\) is semicontinuous with nonempty, compact, \(\infty\)-proximally connected values; here \(C\) is a closed convex subset of \(E\), \(U\) an open bounded subset of \(C\). The authors consider the case when \(T\) is an only countably \(P\)-concentrative map. For such maps \(T\) with \(x \neq Tx\) for \(x \in \partial U\), the index \(I(T,C,R,U)\) is defined in two standard ways; then the existence property, the homotopy property, and the additivity property are proved.
scientific article; zbMATH DE number 2075538
scientific article