Student, who passed the course satisfactorily will be able to:

• understand the geometry and topology of metric spaces in general,
• recognize the metric spaces that are frequently used in mathematics and build metric spaces in relevant cases,
• use the notions of limit, continuity and convergence in metric spaces in context of functions, sequences and series,
• recognize various properties of metric spaces such as connectedness, compactness, totally boundedness etc., and
• use various fundamental theorems regarding the theory of metric spaces, such as Banach's contraction theorem, Arzela-Ascoli theorem, Tietze extension theorem, Baire's category theorem etc.