Topology 1: course

Book

Description

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

Prerequisites

• sets, functions, etc,
• calculus (parts of),
• proofs.

Lectures

The links below are outdated.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
• Introduction to point-set topology
• Neighborhoods and topologies
• Open and closed sets in Rⁿ
• Relative topology and topological spaces
• Continuous functions (maps)
• Compactness
• Separation axioms
• New topological spaces from old:
  • subspaces,
  • product spaces
  • quotient spaces
• Homotopy
• Cell complexes

• Point-set topology: exercises

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.

Also

• Point-set topology: course
• Topology 2: course