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Axioms 2018, 7(2), 34;

Pre-Metric Spaces Along with Different Types of Triangle Inequalities

Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Received: 25 April 2018 / Revised: 19 May 2018 / Accepted: 21 May 2018 / Published: 24 May 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
Full-Text   |   PDF [249 KB, uploaded 24 May 2018]


The T 1 -spaces induced by the pre-metric spaces along with many forms of triangle inequalities are investigated in this paper. The limits in pre-metric spaces are also studied to demonstrate the consistency of limit concept in the induced topologies. View Full-Text
Keywords: quasi-metric space; Hausdorff space; T1-space; triangle inequalities quasi-metric space; Hausdorff space; T1-space; triangle inequalities
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wu, H.-C. Pre-Metric Spaces Along with Different Types of Triangle Inequalities. Axioms 2018, 7, 34.

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