A construction of the B-completion of a T-0-quasi-metric space

作者：Kuenzi Hans Peter A

来源：Topology and Its Applications, 2014, 170: 25-39.

DOI：10.1016/j.topol.2014.03.017

• T-0-quasi-metric space
• Injective hull
• q-Hyperconvex
• Doitchinov completion
• Balanced
• Cauchy filter pair
• Dedekind-MacNeille completion

We present a construction of the B-completion of a T-0-quasi-metric space (X, d) that is based on the injective hull of (X, d). The B-completion of a T-0-quasi-metric space (X, d) is a T-0-quasi-metric extension of (X, d) studied by H-PA. Kunzi and C. Makitu Kivuvu.
In general, the B-completion of a T-0-quasi-metric space is larger than the better known bicompletion of (X, d). In the special case of a balanced T-0-quasi-metric space the B-completion coincides with a completion that was first investigated by D. Doitchinov.
Among other things, in this note we show that the B-completion of the natural T-0-quasi-metric of a partially ordered set (possessing a smallest and a largest element) can be identified with the Dedekind-MacNeille completion of that partially ordered set.

• 出版日期2014-6-15