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Simply connected space
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<p>In <a href="/facts/Topology/2EqW47cU">topology</a>, a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> is called simply connected (or 1-connected, or 1-simply connected) if it is <a href="/facts/Path-connected/5CUTxfoA">path-connected</a> and every <a href="/facts/Path_(topology)/MkKRCYXT">path</a> between two points can be continuously transformed into any other such path while preserving the two endpoints in question. Intuitively, this corresponds to a space that has no disjoint parts and no holes that go completely through it, because two paths going around different sides of such a hole cannot be continuously transformed into each other. The <a href="/facts/Fundamental_group/VyYtLqSP">fundamental group</a> of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected if and only if its fundamental group is trivial. </p>