Topological Pair
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, more specifically algebraic topology, a pair (X,A) is short-hand for an inclusion of topological spaces icolon Ahookrightarrow X. Sometimes i is assumed to be a cofibration. A morphism from (X,A) to (X'',A'') is given by two maps fcolon Xrightarrow X'' and gcolon Arightarrow 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.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, more specifically algebraic topology, a pair (X,A) is short-hand for an inclusion of topological spaces icolon Ahookrightarrow X. Sometimes i is assumed to be a cofibration. A morphism from (X,A) to (X'',A'') is given by two maps fcolon Xrightarrow X'' and gcolon Arightarrow 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.