Introduction to topology

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Introduction to topology

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 2	2 + 3	exam + term grade	pure math.	mm1c1to3m mm1c2to3m	3	compulsory

Course coordinator

András Szűcs
Department of Analysis
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
		Weak: Analysis3P-p (mm1c2an3m)
		Strong: Algebra2L (mm1c1al2)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

András Szűcs, Department of Analysis, Institute of Mathematics.

Literature

Recommended:

J. L. Kelley: General Topology. 1957, Princeton.

Syllabus

Topological spaces and continuous functions. Constructions: subspaces, factor spaces, product spaces. Separation axioms. Urysohn's lemma. The Tietze extension theorem. Countability axioms. Lindelöf's theorem. Compactness. Compact metric spaces. The Tychonoff theorem. Connectedness. Simplicial complexes. The Euler characteristics.
CW complexes. Homotopy, loops, fundamental group. Covering spaces.
Applications: The fundamental theorem of algebra. Brouwer fixed point theorem. The hedgehog theorem.