TITLE: What's the precise meaning of the expression "induced by" in mathematics?
QUESTION [17 upvotes]: It's been more than once I've found this expression "induced by", in a sentence of the form "$X$ is induced by $Y$, in mathematics and computer science. I usually associate "induced by" with "generated by". However, I am not always confident regarding its meaning. 
For example, in the following sentence

If a planar subdivision is induced by $n$ line segments...

What's the precise meaning of "induced by", in general, and in the sentence above?

REPLY [5 votes]: In the specific case, the $n$ line segments can be extended uniquely to lines, that give a planar subdivision (Edit: see comments below). In general, as mentioned in the comments, there is no literal interpretation that always works. Sometimes we have a "smaller" thing that can be extended uniquely (as in this case), sometimes we have a " bigger" thing that can be reduced uniquely (as for the induced or relative topology on a subset of a topological space), and sometimes neither of the two. A good use of the word requires that it is clear from the context what is meant. The idea is always to adapt /modify something given in a canonical / unique way to get what we need.