First-countable, Sequential, and Frechet Spaces

This article contains a definition of three classes of topological spaces: first-countable, Frechet, and sequential. Next there are some facts about them, that every first-countable space is Frechet and every Frechet space is sequential. Next section constains a formalized construction of topological space which is Frechet but not first-countable. This article is based on [9, pp. 73–81].