Displaying similar documents to “On a fixed-point theorem of Banach-type for uniform spaces”

The compact weak topology on a Banach space.

Manuel González, Joaquín M. Gutiérrez (1990)

Extracta Mathematicae

Similarity:

Throughout [this paper], E and F will denote Banach spaces. The bounded weak topology on a Banach space E, noted bw(E) or simply bw, is defined as the finest topology that agrees with the weak topology on bounded sets. It is proved in [3] that bw(E) is a locally convex topology if and only if E is reflexive. In this paper we introduce the compact weak topology on a Banach space E, noted kw(E) or simply kw, as the finest topology that agrees with the weak topology on weakly...

Regulated functions

Dana Fraňková (1991)

Mathematica Bohemica

Similarity:

The first section consists of auxiliary results about nondecreasing real functions. In the second section a new characterization of relatively compact sets of regulated functions in the sup-norm topology is brought, and the third section includes, among others, an analogue of Helly's Choice Theorem in the space of regulated functions.

C(K) spaces which cannot be uniformly embedded into c₀(Γ)

Jan Pelant, Petr Holický, Ondřej F. K. Kalenda (2006)

Fundamenta Mathematicae

Similarity:

We give two examples of scattered compact spaces K such that C(K) is not uniformly homeomorphic to any subset of c₀(Γ) for any set Γ. The first one is [0,ω₁] and hence it has the smallest possible cardinality, the other one has the smallest possible height ω₀ + 1.

Uniqueness of the topology on L¹(G)

J. Extremera, J. F. Mena, A. R. Villena (2002)

Studia Mathematica

Similarity:

Let G be a locally compact abelian group and let X be a translation invariant linear subspace of L¹(G). If G is noncompact, then there is at most one Banach space topology on X that makes translations on X continuous. In fact, the Banach space topology on X is determined just by a single nontrivial translation in the case where the dual group Ĝ is connected. For G compact we show that the problem of determining a Banach space topology on X by considering translation operators on X is...