In mathematics, particularly algebraic topology, a pair of spaces is an ordered pair (X, A) where X is a topological space and A a subspace (with the subspace topology).
The use of pairs of spaces is sometimes more convenient and technically superior to taking a quotient space of X by A. Pairs of spaces occur centrally in relative homology.
A related concept is that of a triple (X, A, B), with B ⊂ A ⊂ X. Triples are used in homotopy theory. Often, for a pointed space with basepoint at x0, one writes the triple as (X, A, B, x0), where x0 ∈ B ⊂ A ⊂ X.
Famous quotes containing the words pair of, pair and/or spaces:
““You know,” said the Finn, “I got a pair of shoes older than you are.””
—William Gibson (b. 1948)
“When strength is yoked with justice, where is a mightier pair than they?”
—Aeschylus (525–456 B.C.)
“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)