Homotopy theory | Properties of topological spaces | Algebraic topology
Semi-locally simply connected
In mathematics, specifically algebraic topology, semi-locally simply connected is a certain local connectedness condition that arises in the theory of covering spaces. 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 correspondence between covering spaces and subgroups of the fundamental group. Most “nice” spaces such as manifolds and CW complexes are semi-locally simply connected, and topological spaces that do not satisfy this condition are considered somewhat pathological. The standard example of a non-semi-locally simply connected space is the Hawaiian earring. (Wikipedia).
