Point-set topology: course
From Intelligent Perception
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 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.