Definition:Topology (Mathematical Branch)
Definition
Topology is a geometry of transformations in which the only invariant is continuity.
Some sources suggest that it can indeed be described simply as the study of continuity.
As such, it is closely interwoven with the branch of analysis.
Also known as
The original name of the mathematical branch known as topology was geometria situs, or analysis situs (that is: geometry / analysis of position).
It is often referred to as rubber-sheet geometry.
Also see
- Results about topology can be found here.
Historical Note
The mathematical branch known as topology originally arose as a sub-branch of geometry.
However, it has since evolved such that it contributes to many other mathematical branches.
Linguistic Note
The word topology is derived from the Greek words τόπος, meaning place, and λόγος, meaning study.
This originates from its origins as the study of situation.
The word topology was coined by Johann Benedict Listing in a letter of $1836$.
The word was first published in the title of Listing's $1847$ book Vorstudien zur Topologie, but never caught on until the $1920$s.
Sources
- 1959: E.M. Patterson: Topology (2nd ed.) ... (previous) ... (next): Chapter $\text I$: Introduction
- 1964: Peter Freyd: Abelian Categories ... (next): Introduction
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (next): Chapter $1$: Theory of Sets: $\S 1$: Introduction
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): topology
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): topology