Topological Spaces: open sets, closed sets, neighbourhoods, bases, subbases, limit points, closures, interiors, continuous functions, homeomorphisms.
Examples of topological spaces: subspace topology, product topology,metric topology, order topology, topological groups.
Quotient topology, examples of quotient topology: construction of cylinder, cone, suspension, Moebius band, torus, orbit spaces.
Connectedness and Compactness: Connected spaces, Components, Local connectedness, Compact spaces, Local compactness, Tychnoff Theorem. Separation Axioms, Urysohn lemma, Urysohn Metrization theorem,Tietze Extension theorem, One-point compactification, paracompactness and partition of unity.
1. J. Dugundji, Topology, UBS, 1999.
2. M. A. Armstrong, Basic Topology, Springer, 2005.
1. J. R. Munkres, Topology: A First Course, Prentice Hall, 1975.
2. G. F. Simmons: Introduction to Topology and Modern Analysis, Tata McGraw-Hill, 1963.