Is there a term for the property of shapes that wraps back into itself?

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If you had a line segment and wanted it to wrap back into itself, you can join the two end and form a circle. You can do the same for a restricted plane into a sphere or torus.

Is there a name for the property of shapes joining back into itself? I was thinking perhaps "modular" from modular arithmetic but that has another meaning when referring to shapes.

Any help would be much appreciated, thanks!

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Take a look at quotient spaces.