topology

MATH101 Topology

Syllabus:

Unit I: Topological spaces: Topological spaces, basis for a given topology, topologizing of sets, elementary concepts, continuous maps, piecewise definition of maps, open maps, closed maps and homeomorphism

Chapter III, Sections 1-4,7-9,11,2

Unit II: Cartesian Products and Connectedness: Cartesian product topology, continuity of maps, slices in Cartesian products; connectedness, applications, components, local connectedness and path-connectedness

Chapter IV, Sections 1-3 and Chapter V, Sections 1-5

Unit III: Quotient topology, Compactness and Local Compactness: Contents??

Chapter V, Sections 1-4, and some selected results from Sections 6,7

Unit IV: Separability, Countability and Convergence: Hausdorff spaces, first and second countable spaces, separable, Lindeloff spaces, nets

Chapter VII, Section 1; Chapter VIII, Section 6,7; Chapter X, Section 6.

Textbooks:

• • J. Dugundji, Topology, Universal Book Stall, New Delhi, 2002

  • G. E. Breadon, Topology and Geometry, Springer

  • A course page on Topology is here

  • WikiBook on Topology is here