The Properties of Supercondensed Sets, Subcondensed Sets and Condensed Sets

We formalized the article “New concepts in the theory of topological space – supercondensed set, subcondensed set, and condensed set” by Yoshinori Isomichi [4]. First we defined supercondensed, subcondensed, and condensed sets and then gradually, defining other attributes such as regular open set or regular closed set, we formalized all the theorems and remarks that one can find in Isomichi’s article. In the last section, the classification of subsets of a topological space is given, depending on the inclusion relation between the interior of the closure and the closure of the interior of a given subset.