In mathematics, specifically algebraic topology, the phrase semi-locally simply connected refers to 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.
Read more about Semi-locally Simply Connected: Definition, Examples, Topology of Fundamental Group
Famous quotes containing the words simply and/or connected:
“The Christian always swears a bloody oath that he will never do it again. The civilized man simply resolves to be a bit more careful next time.”
—H.L. (Henry Lewis)
“Religious fervor makes the devil a very real personage, and anything awe-inspiring or not easily understood is usually connected with him. Perhaps this explains why, not only in the Ozarks but all over the State, his name crops up so frequently.”
—Administration in the State of Miss, U.S. public relief program (1935-1943)