On the metrizability ofkω-spaces

Metrizability of Decomposition Spaces

Simultaneous Metrizability of Coarse Spaces

A metric space can be naturally endowed with both a topology and a coarse structure. We examine the converse to this. Given a topology and a coarse structure we give necessary and sufficient conditions for the existence of a metric giving rise to both of these. We conclude with an application to the construction of the coarse assembly map.

Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

On the Metrizability of Spaces with a Sharp Base

A base B for a space X is said to be sharp if, whenever x ∈ X and (Bn)n∈ω is a sequence of pairwise distinct elements of B each containing x, the collection { ⋂ j≤n Bj : n ∈ ω} is a local base at x. We answer questions raised by Alleche et al. and Arhangel’skĭı et al. by showing that a pseudocompact Tychonoff space with a sharp base need not be metrizable and that the product of a space with a ...

Metrizability of Topological Semigroups on Linearly Ordered Topological Spaces

The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...