Circle ($S^1$, 1-sphere)

The circle is the subspace $S^1=\{z\in \mathbb{C}:|z|=1\}$, equivalently the quotient of a closed interval obtained by identifying its endpoints.

"Circle" can refer to several different concepts or entities, depending on the context: 1. **Geometric Shape**: In mathematics, a circle is a simple shape consisting of all points in a plane that are at a given distance (radius) from a fixed point (center). 2. **Circle in Geometry**: In geometry, a circle is defined by a set of points equidistant from a common center.