Either-or topology
Encyclopedia
In mathematics
, the either–or topology is a topological structure
defined on the closed interval [−1, 1] by declaring a set open
if it either does not contain {0} or does contain (−1, 1).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the either–or topology is a topological structure
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
defined on the closed interval [−1, 1] by declaring a set open
Open set
The concept of an open set is fundamental to many areas of mathematics, especially point-set topology and metric topology. Intuitively speaking, a set U is open if any point x in U can be "moved" a small amount in any direction and still be in the set U...
if it either does not contain {0} or does contain (−1, 1).