TITLE: What "general" in "general topology" refers to
QUESTION [9 upvotes]: What does general in general topology really refer to? We use the term all the time without thinking about its origin.

REPLY [4 votes]: Wikipedia says:
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them. It is distinct from other branches of topology in that the topological spaces may be very general, and do not have to be at all similar to manifolds.
...
Other main branches of topology are algebraic topology, geometric topology, and differential topology. As the name implies, general topology provides the common foundation for these areas.