All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 51

Showing per page

The Banach contraction mapping principle and cohomology

Ludvík Janoš (2000)

Commentationes Mathematicae Universitatis Carolinae

By a dynamical system ( X , T ) we mean the action of the semigroup ( ℤ + , + ) on a metrizable topological space X induced by a continuous selfmap T : X → X . Let M ( X ) denote the set of all compatible metrics on the space X . Our main objective is to show that a selfmap T of a compact space X is a Banach contraction relative to some d 1 ∈ M ( X ) if and only if there exists some d 2 ∈ M ( X ) which, regarded as a 1 -cocycle of the system ( X , T ) × ( X , T ) , is a coboundary.

The fixed point property for some cartesian products

Roman Mańka (2001)

Fundamenta Mathematicae

It is proved that the cylinder X × I over a planar λ-dendroid X has the fixed point property. This is a partial solution of two problems posed by R. H. Bing (cf. [1], Questions 9 and 10).

The fixed-point property for deformations of tree-like continua

Charles Hagopian (1998)

Fundamenta Mathematicae

Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined...

Currently displaying 1 – 20 of 51

Page 1 Next