Syllabus

Unit-I	Topological spaces, basis, subbasis, the product topology on $X \times Y$, the subspace topology, closed sets, closure and interior, limit points, boundary of a set.
Unit-II	Hausdorff spaces, convergent sequence, $T_1$-space, Continuous functions, homeomorphisms, constructing continuous functions, pasting lemma, metric topology, diameter and bounded sets, bounded metric $\overline{d}$ (excluding norm), continuity in metrizable spaces, the sequence lemma, first countability axiom.
Unit-III	Connected spaces, connected subspaces of the real line, connected components, compact spaces, finite intersection property, Heine-Borel theorem for real line, second countable spaces, separable spaces.
Unit-IV	Regular spaces, Normal spaces, Urysohn’s Lemma (statement only), Tietze’s Extension Theorem (statement only), Complete metric spaces, Cantor’s intersection theorem, Baire’s category theorem for complete metric spaces.

Munkres J., Topology: A First Course, (Second Edition), Prentice Hall of India Pvt. Ltd. New Delhi, 2003.
Simmons G.F., Introduction to Topology and Modern Analysis, McGraw-Hill Co., Tokyo, 1963.
Willard S., General Topology, Dover Publication, 2004.
Kelley J., General Topology, Graduate Texts in Mathematics, Springer-Verlag, 1975.

Lecture Notes

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