High Quality Content by WIKIPEDIA articles! In topology, a topological space is called simply connected (or 1-connected) if it is path-connected and every path between two points can be continuously transformed, staying within the space, into every other while preserving the two endpoints in question (see below for an informal discussion). If a space is not simply connected, it is convenient to measure the extent to which it fails to be simply connected; this is done by the fundamental group. Intuitively, the fundamental group measures how the holes behave on a space; if there are no holes, the fundamental group is trivial - equivalently, the space is simply connected.

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