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

- open and closed sets;
- compact spaces;
- continuous functions;
- convergence of sequences, netss, and filterss
- separation axioms

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