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A fixed point theorem for nonexpansive compact self-mapping

T. D. Narang (2014)

Annales UMCS, Mathematica

A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject

A fixed point theorem for non-self multi-maps in metric spaces

Bapurao Chandra Dhage (1999)

Commentationes Mathematicae Universitatis Carolinae

A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].

A fixed-point anomaly in the plane

Charles L. Hagopian, Janusz R. Prajs (2005)

Fundamenta Mathematicae

We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.

A forcing construction of thin-tall Boolean algebras

Juan Martínez (1999)

Fundamenta Mathematicae

It was proved by Juhász and Weiss that for every ordinal α with 0 < α < ω 2 there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that κ < κ = κ and α is an ordinal such that 0 < α < κ + + , then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all α < κ + + , we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic...

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