Area of Mathematics:Analysis
Semester:4ο
Course ID: 41101
Course Type:Compulsory
Teaching hours per week:Theory: 4Practice: 1Laboratory: 0
ECTS :6
Eclass:For the course’s material, click here.
Instructors:Nikolaos Tsirivas
  • Metric spaces: Definitions, basic properties and examples, topological concepts.
  • Sequences in metric spaces, convergent sequences.
  • Bounded and totally  bounded  sets. Compact metric spaces, examples.
  • Characterization of compact metric spaces.
  • Connectivity, connected components, examples.
  • Complete metric spaces: Definition, basic properties, examples. Cantor and Baire theorems, applications.
  • Equivalent metrics,  relative metric,  Separability.
  • Limits of functions, continuity of functions in metric spaces, properties of continuous functions. Uniform continuity. Isometries, Lipschitz functions, Isomorphisms.
  • Fixed point Theorem and applications in algebraic and differential equations.
  • Cartesian products of  metric spaces, examples, applications.