, 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:
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.
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