Topological space
A set with a structure defining closeness without distance.
A topological space is a set equipped with a structure called a topology, which defines the notion of closeness without requiring a numeric distance. It is the most general type of mathematical space that allows for the definition of limits, continuity, and connectedness, and is fundamental to virtually every branch of modern mathematics.
- First defined by
- Maurice Fréchet and Frigyes Riesz
Lore & Background
The concept of topological space evolved from earlier work on surfaces and polyhedra. Möbius and Jordan were among the first to realize that the main problem about the topology of surfaces is to find invariants to decide whether two surfaces are homeomorphic.
Reader's Guide
In the 1930s, James Waddell Alexander II and Hassler Whitney expressed the idea that a surface is a topological space that is locally like a Euclidean plane. The study of topological spaces in their own right is called general topology or point-set topology.
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