for X being non empty TopSpace
for R being non empty SubSpace of R^1
for A being non empty finite set
for F being ManySortedFunction of A st ( for a being set st a in A holds
F . a is continuous Function of X,R ) holds
ex f being continuous Function of X,R st
for x being Point of X
for S being non empty finite Subset of REAL st S = rng ((commute F) . x) holds
f . x = max S