A structure on a mathematical object may naturally introduce a structure to subsets or related sets; that inherited structure is commonly referred to as ‘induced’. Likewise a function between sets might naturally give rise to or ‘induce’ other functions between related sets.

For example, a metric on a set induces a metric on each subset and the topology on a set induces the subspace topology on a subset; a function between sets induces a function between their power sets; a continuous function between two spaces induces a homomorphism between their fundamental groups.