Relation To Topologically Distinguishable Points
Given a topological space X, two points x and y are topologically distinguishable if there exists an open set that one point belongs to but the other point does not. If x and y are topologically distinguishable, then the singleton sets {x} and {y} must be disjoint. On the other hand, if the singletons {x} and {y} are separated, then the points x and y must be topologically distinguishable. Thus for singletons, topological distinguishability is a condition in between disjointness and separatedness.
For more about topologically distinguishable points, see Topological distinguishability.
Read more about this topic: Separated Sets
Famous quotes containing the words relation to, relation and/or points:
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“Art should exhilarate, and throw down the walls of circumstance on every side, awakening in the beholder the same sense of universal relation and power which the work evinced in the artist, and its highest effect is to make new artists.”
—Ralph Waldo Emerson (1803–1882)
“He is the best sailor who can steer within the fewest points of the wind, and extract a motive power out of the greatest obstacles. Most begin to veer and tack as soon as the wind changes from aft, and as within the tropics it does not blow from all points of the compass, there are some harbors which they can never reach.”
—Henry David Thoreau (1817–1862)