This course is for T. Y. B. Sc. Mathematics SEMESTER V (Topology of Metric Spaces)
This course introduces students to the idea of metric spaces. It extends the ideas of
open sets, closed sets, and continuity to the more general setting of metric spaces along
with concepts such as compactness and connectedness. Convergence concepts of sequences
and series of functions, power series are also dealt with. Formal proofs are given a lot of
emphasis in this course. This course serves as a foundation for advanced courses in analysis.
Apart from understanding the concepts introduced, the treatment of this course will enable
the learner to explain their reasoning about analysis with clarity and rigor.
