General topology

In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.

The fundamental concepts in point-set topology are continuity, compactness, and connectedness:

The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.

List of examples in general topology

This is a list of useful examples in general topology, a field of mathematics.

See also