mod06lec37 - Connected and Path-connected Components

Connected and path-connected components give us a way to "break-up" a space that is not connected (resp. path-connected), into disjoint pieces which are connected (resp. path-connected). This is done by defining an equivalence relation associated to connected/path-connected subspaces. We give several examples to illustrate the idea, including that of the ordered square and the topologist's sine curve from the previous lecture.