Details

Autor(en) / Beteiligte

• Gaba, Yaé Ulrich
• Künzi, Hans-Peter A.

Titel

Splitting metrics by T0-quasi-metrics

Ist Teil von

• Topology and its applications, 2015-09, Vol.193, p.84-96

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2015

Link zum Volltext

Quelle

Electronic Journals Library - Freely accessible e-journals

Beschreibungen/Notizen

• It is well known that by Szpilrajn's Theorem each partial order on a set can be extended to a linear order. In this paper we study variants of that theorem that hold for T0-quasi-metrics instead of partial orders. More specifically, given a metric space (X,m), we call a T0-quasi-metric d defined on the set X m-splitting provided that its symmetrization ds=d∨d−1 is equal to m. For a given metric space (X,m) we obtain results about T0-quasi-metrics on X that are minimal among the collection of all m-splitting T0-quasi-metrics on X. We are also interested in the maximal possible specialization orders of m-splitting T0-quasi-metrics.