A Stone-Weierstrass theorem for certain discontinuous functions
- 23 Downloads
Let A be point separating unital subalgebra of C(T) where T is a compact metric space. For each bounded function f:T→R which is continuous on the complement of a meagre subset of T there exists a sequence (wn) of elements of the algebra A such that the sequence (wn) convergence uniformly to the function f on each compact subset of the interior of the continuity points of the function f.
KeywordsCompact Subset Hausdorff Space Discontinuous Function Compact Hausdorff Space Continuity Point
Unable to display preview. Download preview PDF.