In math, a **curve** in a space *X* is a mapping from an interval to the space *X*.
In symbols

One -to be more acute- must add that the map gotta be injective and a derivative non-zero

For example if and is a parabola in the 2D euclidean space.

A **curve** -whether it lives- is as slim as the real line at least
locally. That is why a mathematician says that a **curve** is localy
homeomorphic to a 1D **euclidean space**.