The verb "to induce" is used in numerous contexts in mathematics: maps, topologies, etc. In virtually every case, the author seems to take for granted that the reader knows what it means. Sometimes the usage is in a sentence of the form "An X induces a Y by.../in the form of .../etc.," but this is a description of the consequences of a particular instantiation of (this sort of) induction, not a clarification of what it is to "induce" something in general. Online searches for a definition seem always to lead either to definitions of mathematical induction (the proof technique) or to uses of the verb "induces" rather than definitions of it. Can anyone provide a definition and/or provide a specific reference to one? Thanks.