Noncontinuous examples
I want to confirm if I understand "common evaluation" correctly.
So I describe two examples. Please say me if I misunderstand.
The definition oin 5.2 says:
"The common operation instances are those (x1 , x2 , . . . , xk ; y) such that the point
function phi is everywhere defined and continuous on the closed, bounded, nonempty box
(x1 , x2 , . . . , xk ), and y equals the range of phi over this box."
It says "phi is continous" not "restriction of phi is continous".
I guess that this is reserved for possible cset flavour.
I try to interpret this definition for floor(x) and case(c,g,h).
1) The only common evaluations of float(x) are
([a,b] ; [k.k] ) where k < a <= b < k + 1 , k \in Z .
Pair ([0,0]; [0,0]), is not common evaluation because float(x) is discontinous at 0 .
2) The only common evaluations of case(c,g,h) are
i) ([a,b],[c,d],[e,f]; [c,d] ) where 0 < a <= b , c <= d, e <= f
ii) ([a,b],[c,d],[e,f]; [e,f]) where a <= b < 0, c <= d, e <= f
iii) ([a,b],[c,c],[c,c]; [c,c]) where a <= b
Pair ([0,1],[2,2],[2,3]; [2,2]) is not common evaluation because case(c,g,h) is discontinous at (0,2,3) .
Is definition of common evaluation for case(c,g,h) is different from other point functions ?
-Dima