# 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**).

## 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