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Extenders for vector-valued functions

Iryna Banakh, Taras Banakh, Kaori Yamazaki (2009)

Studia Mathematica

Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender u : C ∞ ( A , Y ) → C ∞ ( X , Y ) , which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained allow us...

Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2 X can be extended to a Whitney map for 2 X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Extending real-valued functions in βκ

Alan Dow (1997)

Fundamenta Mathematicae

An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality c and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Extending the ideal of nowhere dense subsets of rationals to a P-ideal

Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2013)

Commentationes Mathematicae Universitatis Carolinae

We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, F σ ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).

Extension of functions with small oscillation

Denny H. Leung, Wee-Kee Tang (2006)

Fundamenta Mathematicae

A classical theorem of Kuratowski says that every Baire one function on a G δ subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer gradation of Baire one functions into small Baire classes. A Baire one function f is assigned into a class in this hierarchy depending on its oscillation index β(f). We prove a refinement of Kuratowski’s theorem: if Y is a subspace of a metric space X and f is a real-valued...

Extension of Lipschitz functions defined on metric subspaces of homogeneous type.

Alexander Brudnyi, Yuri Brudnyi (2006)

Revista Matemática Complutense

If a metric subspace Mº of an arbitrary metric space M carries a doubling measure μ, then there is a simultaneous linear extension of all Lipschitz functions on Mº ranged in a Banach space to those on M. Moreover, the norm of this linear operator is controlled by logarithm of the doubling constant of μ.

Currently displaying 241 – 260 of 313