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TY - JOUR TI - On first countable and minimal topological spaces PY - %2022/%12/%18 Y2 - %2025/%12/%22 JF - مجلة المنصور JA - مجلة المنصور VL - 11 IS - 1 LA - en UR - https://journal.muc.edu.iq/journal/article/view/287 SP - 43-55 AB - 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 ER -