Editing Simply connected space (section)

{{short description|Space which has no holes through it}}
In [[topology]], a [[topological space]] is called '''simply connected''' (or '''1-connected''', or '''1-simply connected'''<ref>{{Cite web|url=https://ncatlab.org/nlab/show/n-connected+space|title=n-connected space in nLab|website=ncatlab.org|access-date=2017-09-17}}</ref>) if it is [[path-connected]] and every [[Path (topology)|path]] 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 [[fundamental group]] 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.