TO GET A GOOD UNDERSTANDING OF THE CONCEPTS AND METHODS OF GENERAL TOPOLOGY, WITH PARTICULAR EMPHASIS ON THE MAIN PROPERTIES OF TOPOLOGICAL SPACES LIKE COMPACTNESS AND CONNECTEDNESS.
TO INTRODUCE THE STUDENT TO THE FIRST ELEMENTS OF ALGEBRAIC TOPOLOGY, WITH THE INTRODUCTION OF THE FUNDAMENTAL GROUP E AND THE TOPOLOGICAL CLASSIFICATION OF CURVES AND SURFACES.
TO INTRODUCE THE STUDENT TO THE FIRST ELEMENTS OF ALGEBRAIC TOPOLOGY, WITH THE INTRODUCTION OF THE FUNDAMENTAL GROUP E AND THE TOPOLOGICAL CLASSIFICATION OF CURVES AND SURFACES.
teacher profile teaching materials
Continuous functions, products of topological spaces, Hausdorff spaces, metric spaces, compact spaces, Tychonoff's theorem.
Homotopic equivalente and fundamental group of topological spaces. Coverings.
M. Manetti: Topologia, Springer, 2014.
A. Hatcher: Algebraic Topology, Cambridge University Press, 2002
Programme
Topological spaces and their properties.Continuous functions, products of topological spaces, Hausdorff spaces, metric spaces, compact spaces, Tychonoff's theorem.
Homotopic equivalente and fundamental group of topological spaces. Coverings.
Core Documentation
J. R. Munkres: Topology: a first course, Prentice Hall, 1974.M. Manetti: Topologia, Springer, 2014.
A. Hatcher: Algebraic Topology, Cambridge University Press, 2002
Reference Bibliography
J. R. Munkres: Topology: a first course, Prentice Hall, 1974. M. Manetti: Topologia, Springer, 2014. A. Hatcher: Algebraic Topology, Cambridge University Press, 2002Type of evaluation
Exercises to discuss during the semester, written proof and possibly an oral exam.