Connected Space
Connected and disconnected subspaces of R²
The green space A at top is simply connected whereas the blue space B below is not connected. The pink space C at top and the orange space D are both connected; C is also simply connected while D is not.In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets. Connectedness is one of the principal topological properties that is used to distinguish topological spaces. A stronger notion is that of a path-connected space, which is a space where any two points can be joined by a path.
A subset of a topological space X is a connected set if it is a connected space when viewed as a subspace of X.
As an example of a space that is not connected, one can delete an infinite line from the plane. Other examples of disconnected spaces (that is, spaces which are not connected) include the plane with a closed annulus removed, as well as the union of two disjoint open disks in two-dimensional Euclidean space.
Read more about Connected Space: Formal Definition, Examples, Path Connectedness, Arc Connectedness, Local Connectedness, Theorems, Graphs, Stronger Forms of Connectedness
Famous quotes containing the words connected and/or space:
“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)
“The woman’s world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.”
—Jeanine Basinger (b. 1936)