TOPOLOGIA GENERALE
Academic Year 2018/2019 - 2° YearCredit Value: 6
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester: 1°
Learning Objectives
Fundamentals of General Topology that are usefull for Analysis and Geometry
- Knowledge and understanding: students must understand thery and proofs of fundamental theorems related to topology; to demonstrate mathematical abilities in reasoning.
-Capacity to apply knowledge and understanding: to demonstrate known mathematical results by new techniques; be able to formalize mathematically problems of moderate difficulty, formulated in the natural language, and to take advantage of this information to clarify them or solve them. The ability to apply knowledge and understanding will be achieved through a method of teaching always centered on the logic-deductive method.
- Communication skills: to be able to present materials and scientific arguments, either verbally or in writing, in a clear and comprehensible manner, also by means of simple multimedia tools; be able to work in groups and operate with defined degrees of autonomy.
- Learning Skills: Having developed the skills needed to build simple applications with autonomy; have a flexible mentality, and be able to fit in easily into work environments, adapting easily to new issues.
Course Structure
The course is structured in participatory lectures and cooperatives- It will aim to ensure consistency between the training objectives and the method used, combining the frontal methodology with the dialogue one but including the possibility of applying knowledge in other disciplinary area .
Detailed Course Content
Definition of topological space. Families of open and closed subsets.Neighborhood system of a point and their properties. Accumulation points. Interior, boundary and clousure of sets. Bases and subbases. Significant examples of topological spaces. Subspaces. Axioms of countability. Metric spaces. Separation axioms. Continuous functions and their properties. Homeomorphisms between topological spaces. Products and quotients of topological spaces. Compact topological spaces, connected and path-connected.
Textbook Information
Titolo: Geometria 2. Autore Edoardo Sernesi. Ed. Bollati Boringhieri.