General topology

In mathematics, general topology or point set topology is that branch of topology which studies elementary properties of topological spaces and structures defined on them. Other main branches of topology are algebraic topology and differential topology.

It's in general topology that basic notions, such as:

• open and closed sets;
• compact spaces;
• continuous functions;
• convergence of sequences, nets, and filters
• separation axioms

are defined and theorems about them are proved. Other more advanced notions also appear, but are usually related directly to these fundamental concepts, without reference to other branches of mathematics.

Standard references

Some standard books on general topology include:

• Bourbaki; Topologie Générale (General Topology); ISBN 0-387-19374-X
• John Kelley; General Topology; ISBN 0-387-90125-6
• James Munkres; Topology; ISBN 0-13-181629-2
• Lynn Steen & Arthur Seebach; Counterexamples in Topology; ISBN 0-486-68735-X