Editing Semi-locally simply connected (section)

==Examples==
[[File:Hawaiian earrings.svg|thumb|The [[Hawaiian earring]] is not semi-locally simply connected.]]

A simple example of a space that is not semi-locally simply connected is the [[Hawaiian earring]]: the [[union (set theory)|union]] of the [[circle]]s in the [[Euclidean plane]] with centers (1/''n'', 0) and [[radius|radii]] 1/''n'', for ''n'' a [[natural number]]. Give this space the [[subspace topology]]. Then all [[neighborhood]]s of the [[Origin (mathematics)|origin]] contain [[circle]]s that are not [[nullhomotopic]].

The Hawaiian earring can also be used to construct a semi-locally simply connected space that is not [[Locally simply connected space|locally simply connected]]. In particular, the [[cone (topology)|cone]] on the Hawaiian earring is [[contractible]] and therefore semi-locally simply connected, but it is clearly not locally simply connected.