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:
“... when you do get a job everybody says, Well, they wanted a black woman, which necessarily puts you on a level where you have to prove yourself above being a woman and being black.... Now, I would say, in certain situations, it helped me simply because I was mildly attractive, not because I was black or a woman. That gets you more mileage than anything else.... God help you if youre not an attractive woman.”
—Theresa Brown (b. 1957)
“I like to see a home like this, a home connected with peoples thoughts and work, things they love.”
—Dewitt Bodeen (19081988)
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (18171862)