Topological Representation of Precontact Algebras and a Connected Version of the Stone Duality Theorem -- I

The notions of a {em 2-precontact space}/ and a {em 2-contact space}/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It is shown that there are bijective correspondences between such kinds of algebras and such kinds of spaces. As applications of the obtained results, we get new connect