Topology
Topologi

MATM16F, 7.5 högskolepoäng

Gäller från och med: Spring 2018
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2018-03-02

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: MATM16
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

Munkres, J.: Topology. Pearson New International Edition. Pearson, 2017. ISBN 9780134689517.
Paperback of second edition from 2000.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, seminarier

Kursens examination

Examinationsformer: Skriftlig tentamen, muntlig tentamen. Compulsory assignments may occur,
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

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

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://www.ctr.maths.lu.se/course/top/