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

\mathrm{curve}:I\to X

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

For example if I=\mathbb{R} and \mathrm{curve}(t)=(t,t^2) is a parabola in the 2D euclidean space.

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

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