Displaying similar documents to “Hyperconvexity of ℝ-trees”

Near metric properties of function spaces

P. Gartside, E. Reznichenko (2000)

Fundamenta Mathematicae

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"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

Teresa Bigorajska, Henryk Kotlarski, James Schmerl (1998)

Fundamenta Mathematicae

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We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.

ℳ-rank and meager groups

Ludomir Newelski (1996)

Fundamenta Mathematicae

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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 ℵ 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

The fixed-point property for deformations of tree-like continua

Charles Hagopian (1998)

Fundamenta Mathematicae

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Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were...

Selections that characterize topological completeness

Jan van Mill, Jan Pelant, Roman Pol (1996)

Fundamenta Mathematicae

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We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].