Page 1 of 1
Show that if Y is compact, then the projection 11 : X Y → X is a closed map. Theorem. Let f :X + Y; let Y be compact Hau
Posted: Wed May 11, 2022 9:28 pm
by answerhappygod
- Show That If Y Is Compact Then The Projection 11 X Y X Is A Closed Map Theorem Let F X Y Let Y Be Compact Hau 1 (60.14 KiB) Viewed 23 times
Show that if Y is compact, then the projection 11 : X Y → X is a closed map. Theorem. Let f :X + Y; let Y be compact Hausdorff. Then f is continuous if and only if the graph of f, Gf = {x x f(x) | X e X}, is closed in X x Y. (Hint: If Gf is closed and V is a neighborhood of f(xo), then the intersection of G f and X ~ (Y – V) is closed. Apply the previous exercise.]