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# Details for Course MATM16F Topology

General
• MATM16F
• Temporary
Course Name
• Topology
Course Extent
• 7.5
Type of Instruction
• Course given jointly for second and third cycle
• 7151 (Centre of Mathematical Sciences / Mathematics)
•  -03-02
• Professor Thomas Johansson

## Current Established Course Syllabus

General
Aim
• 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.
Contents
• 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.
Knowledge and Understanding
• For a passing grade the doctoral student must
• 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.
Competences and Skills
• For a passing grade the doctoral student must
• 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.
Judgement and Approach
• For a passing grade the doctoral student must
Types of Instruction
• Lectures
• Seminars
Examination Formats
• Written exam
• Oral exam
• Compulsory assignments may occur,
• Failed, pass
• FMAA05 Calculus in one variable, FMAB20 Linear algebra, FMAB30 Calculus in several variables , FMAF01 Analytic Functions and FMAF05 Systems and Transforms.
Assumed Prior Knowledge
Selection Criteria
Literature
• Munkres, J.: Topology. Pearson New International Edition. Pearson, 2017. ISBN 9780134689517.
• Paperback of second edition from 2000.
Further Information
Course code
• MATM16F
•  -03-02
• Professor Thomas Johansson

## All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Spring 2018 2018‑01‑25 17:32:10 2018‑02‑08 14:56:51 2018‑03‑02

## Current or Upcoming Published Course Occasion

No matching course occasion was found.

## All Published Course Occasions

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0 course occasions.