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Metric spaces with point character equal to their size

C. Avart, P. Komjath, Vojtěch Rödl (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider the point character of metric spaces. This parameter which is a uniform version of dimension, was introduced in the context of uniform spaces in the late seventies by Jan Pelant, Cardinal reflections and point-character of uniformities, Seminar Uniform Spaces (Prague, 1973–1974), Math. Inst. Czech. Acad. Sci., Prague, 1975, pp. 149–158. Here we prove for each cardinal κ , the existence of a metric space of cardinality and point character κ . Since the point character can...

Metric spaces with the small ball property

Ehrhard Behrends, Vladimir M. Kadets (2001)

Studia Mathematica

A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete metric...

Metric-fine uniform frames

Joanne L. Walters-Wayland (1998)

Commentationes Mathematicae Universitatis Carolinae

A locallic version of Hager’s metric-fine spaces is presented. A general definition of 𝒜 -fineness is given and various special cases are considered, notably 𝒜 = all metric frames, 𝒜 = complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.

Metrizability of σ -frames

M. Mehdi Ebrahimi, M. Vojdani Tabatabaee, M. Mahmoudi (2004)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Metrizable completely distributive lattices

Zhang De-Xue (1997)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.

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