This site contains: mathematics courses and book; covers: image analysis, data analysis, and discrete modelling; provides: image analysis software. Created and run by Peter Saveliev.

From Intelligent Perception

1 Description

This is an introductory, one semester course on point-set/general topology and its applications. Elementary topology. Topics include topologies, separation axioms, connectedness, compactness, continuity, and metric spaces. It is intended for advanced undergraduate and beginning graduate students.

2 Prerequisites

• calculus (parts of),
• proofs.

3 Lectures

• The topology of the Euclidean space
• Topology in calculus
• Metric spaces
• Convergence
• Introduction to point-set topology
• Neighborhoods and topologies
• Open and closed sets in Rⁿ
• Relative topology and topological spaces
• Continuous functions
• Compactness
• Separation axioms
• New topological spaces from old:
  • subspaces,
  • product spaces
  • quotient spaces
• Topological vector spaces

• Point-set topology: exercises

4 Notes

The content is based on the complete set of lecture notes for a course taught by Peter Saveliev in Fall 2009/Spring 2010 at Marshall University.

Texts:

• Introduction to Topology by Gamelin and Greene
• Topology of Surfaces by Kinsey
• Basic Topology by Armstrong