The invariance of domain theorem for condensing vector fields (Q2568597)

In the paper under review, an invariance of domain theorem is presented for a class of countably \(k\)-condensing (\(k\)-set contraction) vector fields, \(k\in [0,1)\), in Banach spaces. As main tools, the author uses a degree theory for countably condensing maps due to \textit{M. Väth} [Topol. Methods Nonlinear Anal. 13, No.~2, 341--363 (1999; Zbl 0964.47025), J. Math. Anal. Appl. 257, No.~1, 223--237 (2001; Zbl 1021.47028)] and Borsuk's theorem for odd countably condensing maps. As immediate consequences, the author obtains results on surjectivity and homeomorphism. The ideas of proofs are taken from analogous results for compact or condensing vector fields.