Definition:Topology (Mathematical Branch)

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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 this subject was geometria situs, or analysis situs (that is: geometry / analysis of position).


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