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Search: MSC category 54E35 ( Metric spaces, metrizability )

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1. CMB 2010 (vol 54 pp. 180)

Spurný, J.; Zelený, M.
Additive Families of Low Borel Classes and Borel Measurable Selectors
An important conjecture in the theory of Borel sets in non-separable metric spaces is whether any point-countable Borel-additive family in a complete metric space has a $\sigma$-discrete refinement. We confirm the conjecture for point-countable $\mathbf\Pi_3^0$-additive families, thus generalizing results of R. W. Hansell and the first author. We apply this result to the existence of Borel measurable selectors for multivalued mappings of low Borel complexity, thus answering in the affirmative a particular version of a question of J. Kaniewski and R. Pol.

Keywords:$\sigma$-discrete refinement, Borel-additive family, measurable selection
Categories:54H05, 54E35

2. CMB 2010 (vol 53 pp. 719)

Stasyuk, I.; Tymchatyn, E. D.
A Continuous Extension Operator for Convex Metrics
We consider the problem of simultaneous extension of continuous convex metrics defined on subcontinua of a Peano continuum. We prove that there is an extension operator for convex metrics that is continuous with respect to the uniform topology.

Categories:54E35, 54C20, 54E40

3. CMB 2008 (vol 51 pp. 413)

Thé, L. Nguyen Van
Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces
Given a countable set $S$ of positive reals, we study finite-dimensional Ramsey-theoretic properties of the countable ultrametric Urysohn space $\textbf{Q} _S$ with distances in $S$.

Keywords:Ramsey theory, Urysohn metric spaces, ultrametric spaces
Categories:05C50, 54E35

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