Properties and principles on partial metric spaces

In this paper, we topologically study the partial metric space, which may be seen as a new sub-branch of the pure asymmetric topology. We show that many familiar topological properties, and principles still hold in certain partial metric spaces, although some results might need some advanced assumptions. Various properties, including separation axioms, countability, connectedness, compactness, completeness and Ekeland's variation principle, are discussed. (C) 2017 Elsevier B.V. All rights reserved.National Natural Science Foundation of China [11201431]; China Postdoctoral Science Foundation [191170]SCI(E)ARTICLE77-9823