x1 (function) is the restriction of function x2 to domain set x3
x3 should normally be a (strict) subset of the domain set of x1; however, for generality, any set is allowed, but x1 will be undefined everywhere except on/in the intersection of x3 with the domain set of x2. Outside of x3, x1 is undefined, even if x2 is. In/on x3, x1 and x2 are identically equal everywhere. x2 is a specific extension of x1. For the sense of restriction in which, instead of being undefined outside of x3, x1 is identically equal to the zero element of the space on the set exclusion of the domain of x2 lacking x3 (and which is undefined everywhere not in the domain set of x2), try to use a product of a zdeltakronekre function with x2, which will be defined on the intersection of their two domain sets and will identically be 0 or x2 as specified. Be careful, concerning x3, when the domain set of x2 is the Cartesian product (pi'u) of sets; for example, R is not a subset of R2, even if it is isomorphic to one (actually, uncountably infinitely many in this case).