Definition talk:Loop (Topology)/Topological Manifold

Just being curious here: why does a loop in a topological manifold have to be on a continuous path, but a loop in a general topological space not have to be continuous? --prime mover (talk) 06:20, 16 December 2022 (UTC)


 * Actually, in books by Lee all loops are continuous maps. I understand that the definition given here rests upon Topology by Munkres, and I do not have it at the moment.--Julius (talk) 09:43, 16 December 2022 (UTC)


 * By definition of path, a path is always a continuous mapping. By the general definition of loop, a loop is a path, so a loop is a continuous mapping. Arguably in this definition of loop in topological manifolds, the word continuous is superfluous. --Anghel (talk) 12:22, 16 December 2022 (UTC)


 * Good point. I will check my sources later tonight (probably the author prefers recalling the obvious) and update accordingly.--Julius (talk) 14:22, 16 December 2022 (UTC)