0-connected | path-connected

A topological space X is pathwise-connected iff for every two points x, y element X, there is a continuous function f from [0, 1] to X such that f(0) = x and f(1) = y. Roughly speaking, a space X is pathwise-connected if, for every two points in X, there is a path connecting them. For locally pathwise-connected spaces (which include most "interesting spaces" such as manifolds and CW-complexes), being connected and being pathwise-connected are equivalent, although there are connected spaces which are not pathwise-connected. Pathwise-connected spaces are also called 0-connected.

connected space | convex | CW-complex | locally pathwise-connected | star convex | topological space