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 spaces, especially normed linear spaces, 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 continuity, in a technically adequate form that can be applied in any area of mathematics.
Read more about this topic: General Topology
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