Metric on the Countable Soft Topological Space

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.