Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: metrization

Sortuj według:

Ogranicz wyniki do:

Metrization in small and large scale structures

Miyata T.

Bulletin of the Polish Academy of Sciences. Mathematics

2017

Vol. 65, no. 1

81--92

Given a topological structure and a coarse structure on a set, N. Wright gave a necessary and sufficient condition for the set to have a metric inducing simultaneously both the structures. We use the idea of the Alexandroff and Urysohn metrization theorem for topological spaces, to investigate a simultaneous metrization problem for a set with a uniform (and topological) structure and a coarse structure. In particular, we prove that given two metrics dU and dC on a set X such that the uniform (topological) structure induced by dU is compatible in some sense with the coarse structure induced by dC, there exists a metric d on X which is isometric to dU in a small scale and to dC in a large scale. We then apply this idea to show that if, in addition, the uniform space has uniform dimension 0 and the coarse space has asymptotic dimension 0, then there exists an ultrametric d on X which is isometric to dU in small scale and to dC in large scale.

Domain Theory as a Tool for Topology - a Case Study

Waszkiewicz P.

Schedae Informaticae

2003

Vol. 12

17-26

In this paper we adopt a certain view on continuous posets and see them as models of their spaces of maximal elements, which are most often topologies rich in structure. Adopting this perspective seems to be fruitful: we are often able to match structural properties of the modelling poset to properties of the modelled space. It was discovered by Mike Reed and Keye Martin two years ago that existence of a measurement on the model corresponds to existence of a development for the modelled topological space. We present an elementary proof of this fact and show how one can use this result to give a new proof to one of the first metrization theorems in Topology.