Simply Connected Space
In topology, a topological space is called simply connected (or 1-connected) if it is path-connected and every path between two points can be continuously transformed, staying within the space, into any other path while preserving the two endpoints in question (see below for an informal discussion).
If a space is not simply connected, it is convenient to measure the extent to which it fails to be simply connected; this is done by the fundamental group. Intuitively, the fundamental group measures how the holes behave on a space; if there are no holes, the fundamental group is trivial — equivalently, the space is simply connected.
Read more about Simply Connected Space: Informal Discussion, Formal Definition and Equivalent Formulations, Examples, Properties
Famous quotes containing the words simply, connected and/or space:
“In America, the photographer is not simply the person who records the past, but the one who invents it.”
—Susan Sontag (b. 1933)
“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)
“It is the space inside that gives the drum its sound.”
—Hawaiian saying no. 1189, ‘lelo No’Eau, collected, translated, and annotated by Mary Kawena Pukui, Bishop Museum Press, Hawaii (1983)