This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Point-set topology: course

### From Mathematics Is A Science

## Contents

## 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

## 3 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The links below are outdated.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
- Metric spaces
- Convergence
- Introduction to point-set topology
- Neighborhoods and topologies
- Open and closed sets in
**R**^{n} - Relative topology and topological spaces
- Continuous functions
- Compactness
- Separation axioms
- New topological spaces from old:
- Topological vector spaces

## 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.

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