Exercises:Saul - Algebraic Topology - 5/Exercise 5.6

Exercises

Exercise 5.6

Let $(X,\mathcal{ J })$ be a topological space and let $A\in\mathcal{P}(X)$ be a retract of $X$ (with the continuous map of the retraction being $r:X\rightarrow A$). Lastly take i $i:A\rightarrow X$ to be the inclusion map, $i:a\mapsto a$.

Show that: $H_*^s(X)\cong H_*^s(A)\oplus H_*^s(X,A)$