CODE 25909 ACADEMIC YEAR 2024/2025 CREDITS 8 cfu anno 2 MATEMATICA 8760 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/03 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The course offers an introduction to General Topology. AIMS AND CONTENT LEARNING OUTCOMES The course aims to introduce the student to the foundations of the General Topology, with particular attention to the concepts of continuity, connectivity and compactness. AIMS AND LEARNING OUTCOMES At the end of the course, students will have a good understanding of the fundamental notions of General Topology, such as continuity, separation axioms, connectedness, compactness, metrizability. PREREQUISITES The courses of the first year of our Laurea in Matematica. TEACHING METHODS Traditional method: lectures in presence. SYLLABUS/CONTENT Metric spaces: first properties. Continuous maps between metric spaces; isometries. Topological spaces: first properties. Interior and closure of a subset of a topological space. Bases of open sets and fundamental systems of neighbourhoods. Axioms of countability. Sequences in topological spaces. Continuous maps between topological spaces; homeomorphisms. Subspaces of a topological space. (Arbitrary) productss of tpological spaces. Quotients of topological spaces. Separation axioms (in particular: Hausdorff spaces). Connectedness; local connectedness. Compactness; local compactness. Tychonoff's theorem (for arbitrary products). Countable compactness; sequential compactness. Alexandroff compactification. Equivalence for metrizable spaces of the notions of compactness, countable compactness and sequential compactness. Complete metric spaces. Completion of a metric space. Urysohn's lemma. Urysohn's metrizability theorem. Tietze's theorem. Baire spaces. RECOMMENDED READING/BIBLIOGRAPHY 1. V. Checcucci, A. Tognoli, A. Vesentini, Lezioni di topologia generale, Feltrinelli, 1968; 2. M. Manetti, Topologia, seconda edizione, Springer, 2014; 3. S. Willard, General topology, Dover, 2004. TEACHERS AND EXAM BOARD MATTEO PENEGINI Ricevimento: By appointment. FRANCESCO VENEZIANO Ricevimento: See Aulaweb Exam Board MATTEO PENEGINI (President) FRANCESCO VENEZIANO FABIO TANTURRI (President Substitute) LESSONS Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral exam. ASSESSMENT METHODS The written part of the exam will consist in exercises on the contents of the course. The oral part of the exam will be based on the contents of the course and will assess the overall knowledge of the student. Exam schedule Data appello Orario Luogo Degree type Note 10/01/2025 10:00 GENOVA Scritto 16/01/2025 10:00 GENOVA Orale 05/02/2025 10:00 GENOVA Scritto 07/02/2025 10:00 GENOVA Orale 03/06/2025 10:00 GENOVA Scritto 05/06/2025 10:00 GENOVA Orale 21/07/2025 10:00 GENOVA Scritto 23/07/2025 10:00 GENOVA Orale 05/09/2025 10:00 GENOVA Scritto 09/09/2025 10:00 GENOVA Orale Agenda 2030 - Sustainable Development Goals Quality education