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Extenders for vector-valued functions
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 , 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 continuous functions on X x Y to subsets of βX x βY
Extending Continuous Functions on Zero-Dimensional Spaces.
Extending Linear Space-Valued Functions.
Extending maps from dense subspaces .
Extending monotone mappings
Extension and Selection theorems in Topological spaces with a generalized convexity structure
Extension of bilipschitz maps of compact polyhedra.
Extension of closed mappings
Extension of Lipschitz functions defined on metric subspaces of homogeneous type.
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.
Extension of Lipschitz mappings on metric trees
Extension of measures: a categorical approach
We present a categorical approach to the extension of probabilities, i.e. normed -additive measures. J. Novák showed that each bounded -additive measure on a ring of sets is sequentially continuous and pointed out the topological aspects of the extension of such measures on over the generated -ring : it is of a similar nature as the extension of bounded continuous functions on a completely regular topological space over its Čech-Stone compactification (or as the extension of continuous...
Extension of point-finite partitions of unity
A subspace A of a topological space X is said to be -embedded ((point-finite)-embedded) in X if every (point-finite) partition of unity α on A with |α| ≤ γ extends to a (point-finite) partition of unity on X. The main results are: (Theorem A) A subspace A of X is (point-finite)-embedded in X iff it is -embedded and every countable intersection B of cozero-sets in X with B ∩ A = ∅ can be separated from A by a cozero-set in X. (Theorem B) The product A × [0,1] is (point-finite)-embedded in X...
Extension of sequentially continuous mappings
Extension properties of Stone-Čech coronas and proper absolute extensors
We characterize, in terms of X, the extensional dimension of the Stone-Čech corona βX∖X of a locally compact and Lindelöf space X. The non-Lindelöf case is also settled in terms of extending proper maps with values in , where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a -set X in the Tikhonov cube we find a necessary and sufficient condition, in terms of , for X to be in the class AE([L]). We also introduce a concept of a proper absolute extensor and...
Extension theorem for a pseudo-arc
Extension theory of infinite symmetric products
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension ext-dim(X) was introduced by A. N. Dranishnikov [9] in the context of compact spaces and CW complexes. This paper investigates extension types of infinite symmetric products SP(L). One of the main ideas of the paper is to treat ext-dim(X) ≤ SP(L) as the fundamental concept of cohomological dimension...
Extensions and selections of maps with decomposable values
Extensions of Ćirić generalised contractions