In light of the recent discussion here about the "horizontal line notation", I've returned to the introduction to map objects in L. & S., _Conceptual Mathematics_. This statement is in the rectangle at the top of page 314. ( Script.ChangeFont Courier8 ) T e X ----> Y T x Y ----> Y induces ------------- T x X ----> Y Evaluation map e induces a "correspondence". Is this horizontal line an implication or an equivalence or a map or a bijection? "Induces" seems plausible but exactly what is meant? Thanks, ... Peter E.