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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access May 16, 2017

Versatile asymmetrical tight extensions

Olivier Olela Otafudu and Zechariah Mushaandja

Abstract

We show that the image of a q-hyperconvex quasi-metric space under a retraction is q-hyperconvex. Furthermore, we establish that quasi-tightness and quasi-essentiality of an extension of a T0-quasi-metric space are equivalent.

MSC 2010: 54E40; 54B30

References

[1] Agyingi C.A. , Hyperconvex hulls in categories of quasi-metric spaces, Ph.D. thesis, University of Cape Town, 2014.Search in Google Scholar

[2] Agyingi C.A., Haihambo P., H.-P.A. Künzi, Tight extensions of T0-quasimetric spaces, Ontos-Verlag: Logic, Computations, Hierarchies 2014, 9-22.10.1515/9781614518044.9Search in Google Scholar

[3] Agyingi C.A., Haihambo P., Künzi H.-P.A., Endpoints in T0-quasimetric spaces, Topology Appl., 2014, 168, 82-93.10.1016/j.topol.2014.02.010Search in Google Scholar

[4] Agyingi C.A., Haihambo P., Künzi H.-P.A., Endpoints in T0-quasi-metric spaces, II, Abstract and Applied Analysis (2013), article ID 539573, 10 pages.10.1155/2013/539573Search in Google Scholar

[5] Dress A.W.M., Trees, Tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. Math., 1984, 53, 321-402.10.1016/0001-8708(84)90029-XSearch in Google Scholar

[6] Herrlich H., Hyperconvex hulls of metric spaces, Topology Appl., 1992, 44, 181-187.10.1016/0166-8641(92)90092-ESearch in Google Scholar

[7] Hofmann D., Reis C.D., Probabilistic metric spaces as enriched categories, Fuzzy Sets Syst., 2013, 210, 1-21.10.1016/j.fss.2012.05.005Search in Google Scholar

[8] Kemajou E., Künzi H.-P.A., Olela Otafudu O., The Isbell-hull of a di-space. Topology Appl., 2012, 159, 2463-2475.10.1016/j.topol.2011.02.016Search in Google Scholar

Published Online: 2017-5-16
Published in Print: 2017-4-25

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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