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:
“Raising a daughter is an extremely political act in this culture. Mothers have been placed in a no-win situation with their daughters: if they teach their daughters simply how to get along in a world that has been shaped by men and male desires, then they betray their daughters’ potential But, if they do not, they leave their daughters adrift in a hostile world without survival strategies.”
—Elizabeth Debold (20th century)
“A peasant becomes fond of his pig and is glad to salt away its pork. What is significant, and is so difficult for the urban stranger to understand, is that the two statements are connected by an and and not by a but.”
—John Berger (b. 1926)
“The limitless future of childhood shrinks to realistic proportions, to one of limited chances and goals; but, by the same token, the mastery of time and space and the conquest of helplessness afford a hitherto unknown promise of self- realization. This is the human condition of adolescence.”
—Peter Blos (20th century)