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:
“I do not think the mere extension of the ballot a panacea for all the ills of our national life. What we need to-day is not simply more voters, but better voters.”
—Frances Ellen Watkins Harper (1825–1911)
“I like to see a home like this, a home connected with people’s thoughts and work, things they love.”
—Dewitt Bodeen (1908–1988)
“This moment exhibits infinite space, but there is a space also wherein all moments are infinitely exhibited, and the everlasting duration of infinite space is another region and room of joys.”
—Thomas Traherne (1636–1674)