On first countable and minimal topological spaces (مجلة المنصور, 2022)
In this paper, we study the concept of minimal topological spaces and its relation with first countable space, we prove that if X is first countable completely regular space, then the following are equivalent.• X is first countable and minimal completely regular space.• X is first countable and completely regular – closed space.A first countable and minimal Urysohn is semi regular and Let be a collection of a topological spaces and , then X is first countable and Hausdorff – closed if and only if each x(n) is first countable and Hausdorff – closed