CODE 84327 ACADEMIC YEAR 2017/2018 CREDITS 15 cfu anno 2 MATEMATICA 8760 (L-35) - SCIENTIFIC DISCIPLINARY SECTOR MAT/03 LANGUAGE Italian TEACHING LOCATION MODULES Questo insegnamento è composto da: GEOMETRY 1 GEOMETRY 2 TEACHING MATERIALS AULAWEB AIMS AND CONTENT SYLLABUS/CONTENT Topological spaces, metric spaces and continuous maps: definitions, general properties, examples. Subspaces. Finite products of topological spaces. Quotient topological spaces: examples (projective spaces, spheres, tori,...). Hausdorff spaces. Connected spaces and path-connected spaces, compact spaces, examples: relation with some concepts of Analysis. The theorem of Tychonoff. Locally compact spaces and the compactification theorem of Alexandroff. Locally connected spaces. Complete metric spaces. Urysohn's lemma and Urysohn's metrizability theorem. Tietze's extension theorem. Baire spaces. Homotopy of maps. Retractions and deformations. The fundamental group and simply connected spaces. Examples. Some slementary methods to compute the fundamental group. The fundamental group of spheres and some other spaces. TEACHERS AND EXAM BOARD MATTEO PENEGINI ARVID PEREGO STEFANO VIGNI Exam Board MATTEO PENEGINI (President) STEFANO VIGNI (President) ARVID PEREGO LESSONS LESSONS START The class will start according to the academic calendar. Class schedule GEOMETRY
