Editing Semi-locally simply connected (section)

{{Expert needed|1=Mathematics|date=June 2020|reason=Appears to be too technical for a non-expert}}
In [[mathematics]], specifically [[algebraic topology]], '''semi-locally simply connected''' is a certain [[locally connected space|local connectedness]] condition that arises in the theory of [[covering space]]s. Roughly speaking, a [[topological space]] ''X'' is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in ''X''. This condition is necessary for most of the theory of covering spaces, including the existence of a [[universal cover]] and the [[Galois connection|Galois correspondence]] between covering spaces and [[subgroup]]s of the [[fundamental group]].

Most “nice” spaces such as [[manifold]]s and [[CW complex]]es are semi-locally simply connected, and topological spaces that do not satisfy this condition are considered somewhat [[pathological (mathematics)|pathological]]. The standard example of a non-semi-locally simply connected space is the [[Hawaiian earring]].