Name for a one-dimensional domain/set that is topologically like a circle?

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Is there a special name for a continuous one-dimensional domain/set that wraps around on itself?

Example 1: The set of unit vectors in $\mathbb{R}^2$.

Example 2: The set of points on a square.

Example 3: $[0,2\pi)$ with an additional link between $0$ and $2\pi$.