The Brouwer-Jordan theorem. (English) Zbl 0805.55003

Kulpa, H.

Acta Univ. Carol., Math. Phys. 33, No. 2, 85-90 (1992).

Let \(f: A\to M\), \(A,M\subset \mathbb{R}^ n\) be a mapping, then the author defines a degree function, such that \[ \deg (gf,K,x)= \sum\deg (f,K,M_ s)\cdot \deg(g,M_ s), \] where \(K\) is some compact set, \(M_ s\) is running through all bounded components of \(\mathbb{R}^ n\setminus M\), \(x\) a suitably chosen point. As a corollary the author deduces a function \(c(f)\) being defined for any continuous \(f: K\to K\) having the usual properties of a degree.

Reviewer: F.W.Bauer (Frankfurt / Main)

MSC:

55M25

Degree, winding number

Keywords:

maps between subsets of Euclidean space; degree function