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:
“So in your discussions of the nuclear freeze proposals, I urge you to beware the temptation of pride—the temptation blithely to declare yourselves above it all and label both sides equally at fault, to ignore the facts of history and the aggressive impulses of an evil empire, to simply call the arms race a giant misunderstanding and thereby remove yourself from the struggle between right and wrong, good and evil.”
—Ronald Reagan (b. 1911)
“We can’t nourish our children if we don’t nourish ourselves.... Parents who manage to stay married, sane, and connected to each other share one basic characteristic: The ability to protect even small amounts of time together no matter what else is going on in their lives.”
—Ron Taffel (20th century)