Department of Mathematics

Lecturer	Sameh TAMRABET
Information	Bachelor - Socle Commun Mathématiques et mathématiques appliquées L2 Department of Mathematics Website : https://www.univ-soukahras.dz/en/module/1200 Semester : S3 Unit : UEF313 Credit : 6 Coefficient: 3
Content	Chapter 1: Topological spaces Open, neighborhood, base, and fundamental system Interior and closure Separated space Induced topology Product topology Convergent sequences Continuous functions Homeomorphisms Topology of metric spaces: distance, ball, etc. Uniform continuity Separable metric spaces Chapter 2: Compact spaces Compact topological space Compact metric space Product of compact metric spaces Compact subsets of the real line Continuous functions on a compact set Locally compact spaces Chapter 3: Complete spaces Cauchy sequences Completeness Extension of a uniformly continuous function Fixed points of contractions Chapter 4: Connected spaces Connectedness Locally connected spaces Chapter 5: Normed vector spaces Norms Distance associated with a norm Equivalent norms
Evaluation	Exam: 60% Directed activities: 40% Evaluation method: Mini-quiz: 10 points Participation: 05 points Discipline: 05 points