- #1
CCMarie
- 11
- 1
How do I prove that:
If X and Y are two compact Hausdorff spaces and f : X × Y → R is a continuous function, then f is approximable by ∑ fi gi , wheret f1, ..., fn in X and g1, ..., gn in Y are continuous functions.
As far as I read I need to use the Stone-Weierstarss Theorem to prove this.
I know that if X and Y are compact, X × Y is compact.
I should prove that {∑ fi gi } is a Banach algebra that separates points... and I don't know what I need to prove?
If X and Y are two compact Hausdorff spaces and f : X × Y → R is a continuous function, then f is approximable by ∑ fi gi , wheret f1, ..., fn in X and g1, ..., gn in Y are continuous functions.
As far as I read I need to use the Stone-Weierstarss Theorem to prove this.
I know that if X and Y are compact, X × Y is compact.
I should prove that {∑ fi gi } is a Banach algebra that separates points... and I don't know what I need to prove?