Compact polyhedral pair

Definition
A pair $$(X,A)$$ where $$X$$ is a topological space and $$A$$ is a subspace, is termed a compact polyhedral pair if there is a (finite) simplicial complex $$K$$ with a subcomplex $$L$$, and a triangulation (viz, a homeomorphism) $$h:|K| \to X$$ such that $$h(|L|) = A$$.

Complex polyhedral pairs are important because we can do homology theory for these instead of just for polyhedra.