This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.
Point-set topology: course
From Mathematics Is A Science
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.
The links below are outdated. The source of material is currently in a draft of a book called Topology Illustrated.
- The topology of the Euclidean space
- Topology in calculus
- Metric spaces
- Introduction to point-set topology
- Neighborhoods and topologies
- Open and closed sets in Rn
- Relative topology and topological spaces
- Continuous functions
- Separation axioms
- New topological spaces from old:
- Topological vector spaces
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.