In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point theorems related to diametrically contractive mapping in a complete soft cone metric space.
Elementary soft topology, soft cone metric, soft net, soft cover, soft compactness, soft fixed point
ALTINTAŞ, İSMET and TAŞKÖPRÜ, KEMAL
"Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping,"
Turkish Journal of Mathematics: Vol. 44:
6, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss6/18