A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space with more than one connected component.
A subset 
of the Euclidean plane with more than one element
can always be disconnected by cutting it through with a line (i.e., by taking out
its intersection with a suitable straight line). In fact, it is certainly possible
to find a line 
such that two points of 
lie on different sides of 
. If the Cartesian equation
of 
is
 |
(1)
|
for fixed real numbers 
, then the set 
is disconnected, since it is the union of the two nonempty
open subsets
 |
(2)
|
and
 |
(3)
|
which are the sets of elements of 
lying on the two sides of 
.
