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:
“He is a thinker: which is to say, he knows how to take things more simply than they are.”
—Friedrich Nietzsche (1844–1900)
“Nothing fortuitous happens in a child’s world. There are no accidents. Everything is connected with everything else and everything can be explained by everything else.... For a young child everything that happens is a necessity.”
—John Berger (b. 1926)