Acquire a good knowledge of concepts and methods of general topology, with particular regard to the study of the main properties of topological spaces such as connection and compactness. Introduce the student to the basic elements of algebraic topology, through the introduction of the fundamental group and the topological classification of curves and surfaces.
Curriculum
teacher profile teaching materials
Connected spaces.
Compact spaces.
Metric spaces.
Homotopy equivalence.
Fundamental group.
Covering spaces.
Supplementary book: Topology James R. Munkres - Prentice Hall.
Programme
Topological spaces.Connected spaces.
Compact spaces.
Metric spaces.
Homotopy equivalence.
Fundamental group.
Covering spaces.
Core Documentation
Text: Lezioni di topologia Lucia Caporaso - Disponibile sul Team del corso.Supplementary book: Topology James R. Munkres - Prentice Hall.
Type of evaluation
Written exam and or midterms, and oral examination. teacher profile teaching materials
Programme
Topological spaces and continuous functions, product and Hausdorff spaces, connectedness and path connectedness, compactness, metric spaces and normal spaces, homotopy and fundamental group, covering spaces and computation of fundamental groups.Core Documentation
Lecture notes by Prof. Lucia Caporaso.Type of delivery of the course
In-class lectures with streaming and recording.Attendance
Students are advised to attend classes regularly and to keep up to date with class content and exams.Type of evaluation
Written exam and or midterms, and oral examination. teacher profile teaching materials
Connected spaces.
Compact spaces.
Metric spaces.
Homotopy equivalence.
Fundamental group.
Covering spaces.
Supplementary book: Topology James R. Munkres - Prentice Hall.
Programme
Topological spaces.Connected spaces.
Compact spaces.
Metric spaces.
Homotopy equivalence.
Fundamental group.
Covering spaces.
Core Documentation
Text: Lezioni di topologia Lucia Caporaso - Disponibile sul Team del corso.Supplementary book: Topology James R. Munkres - Prentice Hall.
Type of evaluation
Written exam and or midterms, and oral examination. teacher profile teaching materials
Programme
Topological spaces and continuous functions, product and Hausdorff spaces, connectedness and path connectedness, compactness, metric spaces and normal spaces, homotopy and fundamental group, covering spaces and computation of fundamental groups.Core Documentation
Lecture notes by Prof. Lucia Caporaso.Type of delivery of the course
In-class lectures with streaming and recording.Attendance
Students are advised to attend classes regularly and to keep up to date with class content and exams.Type of evaluation
Written exam and or midterms, and oral examination.