MATM16F

Tillfällig

Topology

7,5

Gemensam kurs, avancerad nivå och forskarnivå

7151 (Matematikcentrum (inst LTH) / Matematik (LTH))

 -03-02

Professor Thomas Johansson

Engelska

Varje vårtermin

The aim of the course is to consolidate and generalize resultats which the student already has encountered in earlier courses in analysis, to equip him or her with an adequate language for higher studies in mathematics, and to develop his or her ability to work with abstract concepts, which are defined through of axioms. In particular the course should form a bridge between the mathematics courses at the Faculty of Engineering and more advanced mathematics courses.

The fundamentals of the theory of metrical, topological and compact spaces. The Tietze extension theorem and Stone-Weierstrass approximation theorem. Elementary properties of Banach and Hilbert spaces.

be able to define and explain basic concepts in general topology, such as topological space, connected space, continuous map…

be able to describe some common classes of av topologies

be able to account for the different ways to define compactness.

be able to prove the theorems in the course

be able to determine if a given family of sets forms a topological space

be able to prove the compactness of a given topological space

be able to actively reason with use of the terms in the course.

Föreläsningar

Seminarier

Skriftlig tentamen

Muntlig tentamen

Compulsory assignments may occur,

Underkänd, godkänd

FMAA05 Calculus in one variable, FMAB20 Linear algebra, FMAB30 Calculus in several variables , FMAF01 Analytic Functions and FMAF05 Systems and Transforms.

Munkres, J.: Topology. Pearson New International Edition. Pearson, 2017. ISBN 9780134689517.

Paperback of second edition from 2000.

MATM16F

 -03-02

Professor Thomas Johansson