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 fetish of the great university, of expensive colleges for young women, is too often simply a fetish. It is not based on a genuine desire for learning. Education today need not be sought at any great distance. It is largely compounded of two things, of a certain snobbishness on the part of parents, and of escape from home on the part of youth. And to those who must earn quickly it is often sheer waste of time. Very few colleges prepare their students for any special work.”
—Mary Roberts Rinehart (1876–1958)
“Painting gives the object itself; poetry what it implies. Painting embodies what a thing contains in itself; poetry suggests what exists out of it, in any manner connected with it.”
—William Hazlitt (1778–1830)