GEOMETRY

GEOMETRY

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iten
Code
84327
ACADEMIC YEAR
2017/2018
CREDITS
15 credits during the 2nd year of 8760 Mathematics (L-35) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/03
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Mathematics)
modules
This unit is composed by:
Teaching materials

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

Exam Board

MATTEO PENEGINI (President)

STEFANO VIGNI (President)

ARVID PEREGO

LESSONS

LESSONS START

 

The class will start according to the academic calendar.

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

GEOMETRY