On 2S-metric spaces

In this paper, we introduce 2-metric spaces in terms of soft points, called 2s-metric spaces, in the soft universe, which is a nonlinear generalization of soft metric spaces. Then we induce a soft topology from a given 2s-metric space and also study some of its topological structures such as open balls, open (closed) sets, completeness and etc. After that, we prove the Cantor’s Intersection Theorem for complete 2s-metric spaces and use it to show that such a space cannot be expressed as a countable union of no-where dense soft sets under some general situations. At the end, we obtain some fixed point results in complete 2s-metric spaces by using Cantor’s theorem.