Editing General topology (section)

== History ==
General topology grew out of a number of areas, most importantly the following:

*the detailed study of subsets of the [[real line]] (once known as the ''topology of point sets''; this usage is now obsolete)
*the introduction of the [[manifold]] concept
*the study of [[metric space]]s, especially [[normed linear space]]s, in the early days of [[functional analysis]].

General topology assumed its present form around 1940. It captures, one might say, almost everything in the intuition of [[continuous function|continuity]], in a technically adequate form that can be applied in any area of mathematics.