Metric Spaces  (Paperback, JOYDEEP SENGUPTA)

• METRIC SPACES : Definition & Example, Bounded, Unbounded & Pseudo-metric, Non-empty • OPEN AND CLOSED SETS : Concepts, Interior points, Exterior points, Frontier points, Limit point, Isolated point, Derived set, Dense sets, Separable set • COMPLETE METRIC SPACE : Sequence, Convergence, Isometry, Completion of a Metric Space, Cauchy Sequence • CONTINUITY : Function, Continuous functions, Algebra of Real/Complex valued functions, Uniform Continuity • CONNECTED METRIC SPACES : Separated sets, Disconnected & Connected Sets/Spaces, Components, Disconnected spaces, Continuity/Connectedness, Real Line • COMPACT METRIC SPACE : Compactness, Lindelof Space, Finite Intersection, Boundedness