In this paper, we assume that dimensions mean the large inductive dimension Ind and the
covering dimension dim. It is well known that IndX= dimX for each metric space XJ Kulesza …

A fixed-point free map f: X→ X is said to be colorable with k colors if there exists a closed
cover C of X consisting of k elements such that C∩ f (C)=∅ for every C in C. It is shown that …

Easier proofs of coloring theorems Page 1 Topology and its Applications 97 (1999) 155–163
Easier proofs of coloring theorems Jan van Mill1 Faculteit Wiskunde en Informatica, Vrije …

In this paper, we study some dynamical properties of fixedpoint free homeomorphisms of
separable metric spaces. For each natural number p, we define eventual colorings within p …

In [6], for each natural number p we defined eventual colorings within p of homeomorphisms
which are generalizations of colorings of fixed-point free homeomorphisms, and we …

A criterion for existence of a fixed point for an affine action of a given group on a compact
convex space is presented. From this we derive that a discrete countable group is amenable …

There is a close relation between the color number of a continuous map $ f\colon X\to X $
without fixed points and the topological dimension. If $ f $ is an involution, the color number …

Ščepin (1974) and Izydorek and Jaworowski (1995, 1996) showed that for each k and n
such that 2k> n there exists a contractible k-dimensional simplicial complex Y and a …

We investigate the color number and genus for fixed-point free maps of order three. A result
that has the flavor of the Ljusternik-Schnirelmann theorem for involutions is established. The …

The Ljusternik–Schnirelmann–Borsuk theorem for antipodal maps on the sphere can be
stated as an intersection property of coverings of the sphere. We generalized this theorem to …