Metric spaces in pure and applied mathematics.
Metric spaces in which a strengthened form of Blumberg's theorem holds
Metric spaces over partially ordered semi-groups
Metric spaces with the small ball property
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...
Metrically generated probabilistic metric spaces
Metric-fine, proximally fine, and locally fine uniform spaces
Metric-fine uniform frames
A locallic version of Hager’s metric-fine spaces is presented. A general definition of -fineness is given and various special cases are considered, notably all metric frames, complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.
Metrics in locally compact groups
Metrische Räume mit einer Elementarlänge.
Metrizability and weight of inverses under confluent mappings
Metrizability, generalized metric spaces and -functions
Metrizability of certain Pixley-Roy spaces
Metrizability of inverse images of metric spaces under open perfect and 0-dimensional mappings
Metrizability of spaces with countably based closed sets
Metrizability of trees
Metrizability of -frames
Metrizabillity of certain quotient space
Metrizable subsets of Moore spaces
Metrization criteria for compact groups in terms of their dense subgroups
According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...
Metrization of Compact Convex Sets.