Take a triple of topological spaces $(X, A, B)$ consists of a topological space $X$ and two subspaces $A,B$ with $B \subseteq A \subseteq X$. Why is the following sequence of pairs exact? $$ 0 \rightarrow (A,B) \xrightarrow{i} (X, B) \xrightarrow{j} (X, A) \rightarrow 0$$ where $i, j = \text{inclusion}$.
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What is your definition of an exact sequence of pairs of spaces? – Eric Wofsey May 27 '16 at 05:26
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@EricWofsey I don't believe an exact sequence of pairs would differ from a regular exact sequence; that is, we need that im(i) = ker(j). – vanderlylic May 27 '16 at 06:21