Gated sets in quasi-metric spaces

In 1987, Dress and Scharlau studied the well-known concept of gated sets in metric spaces in order to investigate projections in Tits buildings. In this article, we introduce analogously the concept gated sets in a T0-quasi-metric space that we call in-gated set. It turns out that in a T0-quasi-metr...

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Bibliographic Details
Published in:Topology and its applications 2019-08, Vol.263, p.159-171
Main Author: Olela Otafudu, Olivier
Format: Article
Language:English
Subjects:
Gated set
Gluing quasi-pseudometric
Isbell-convexity
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Summary:In 1987, Dress and Scharlau studied the well-known concept of gated sets in metric spaces in order to investigate projections in Tits buildings. In this article, we introduce analogously the concept gated sets in a T0-quasi-metric space that we call in-gated set. It turns out that in a T0-quasi-metric space, there is a dual concept which we call outgated set. We use these concepts to extend some classical results on gluing a family of hyperconvex metric spaces along a set such that the resulting space preserves hyperconvexity from a metric point of view to quasi-metric settings.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2019.05.026