Topological pair

In mathematics, more specifically algebraic topology, a pair ${\displaystyle (X,A)}$ is shorthand for an inclusion of topological spaces ${\displaystyle i\colon A\hookrightarrow X}$. Sometimes ${\displaystyle i}$ is assumed to be a cofibration. A morphism from ${\displaystyle (X,A)}$ to ${\displaystyle (X',A')}$ is given by two maps ${\displaystyle f\colon X\rightarrow X'}$ and ${\displaystyle g\colon A\rightarrow A'}$ such that ${\displaystyle i'\circ g=f\circ i}$.

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