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topological pair ：ウィキペディア英語版

topological pair
In mathematics, more specifically algebraic topology, a pair

(X,A)

is shorthand for an inclusion of topological spaces

i\colon A\hookrightarrow X

. Sometimes

i

is assumed to be a cofibration. A morphism from

(X,A)

(X',A')

is given by two maps

f\colon X\rightarrow X'

and

g\colon A\rightarrow A'

such that

i' \circ g =f \circ i

.
Pairs come up mainly in homology theory and cohomology theory, where chains in

A

are made equivalent to 0, when considered as chains in

X

.
Heuristically, one often thinks of a pair

(X,A)

as being akin to the quotient space

X/A

.
There is a functor from spaces to pairs, which sends a space

X

to the pair

(X,\varnothing)

.
==References==

*.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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