to curves or paths in a manifold. One can also define these where the domain is an interval especially the unit interval or where the domain is a circle (equivalently, a periodic path) S1, which yields a loop. These are used to define the fundamental group, chains in homology theory, geodesic curves, and systolic geometry. Embedded paths and loops lead to knot theory, and related structures such as links, braids, and tangles. Metric spaces Riemannian manifolds are special cases of metric spaces, and thus one has a notion of Lipschitz continuity, Hölder condition, together with a coarse structure, which leads to notions such as coarse maps and connections with geometric group theory. See also :Category:Maps of manifolds