Metric on the Countable Soft Topological Space
Li Fu *
School of Mathematics and Statistics, Qinghai Nationalities University Xining, Qinghai 810000, P.R.China.
Hua Fu
Fujian Police College, Fujian, Fuzhou, 350008, P.R.China.
*Author to whom correspondence should be addressed.
Abstract
The author, ATHAR KHARAL, defined the Euclidean distance using the symmetric difference of sets in soft space, however, we conclude that all the sets of "ε-approximate elements among the soft sets can't calculate their symmetric di erence in this way. To illustrate our point, in this paper, we define the finite(countable) soft topological space, and point out the Euclidean distance given by ATHAR KHARAL can just be applied to the countable soft space. Meanwhile, we give the general definition of the metric soft topological space, test the Euclidean distance being a metric in a countable soft topological space, and achieve a metric countable soft topology.
Keywords: Metric, soft topological space, countable soft topology, Euclidean distance, metric soft space