10. Here is a theorem about compactly generated spaces. We say that f: X --→ Y is a proper map if for each compact set Din Y, the set f-"(D) is compact in X. Theorem. Let X be a space; let Y be a compactly generated Hausdorff space, ISS:X → Y is continuous, injective, and proper, then f is an imbedding and f(X) is closed in Y.

10. Here is a theorem about compactly generated spaces. We say that f: X --→ Y is a proper map if for each compact set Din Y, the set f-"(D) is compact in X. Theorem. Let X be a space; let Y be a compactly generated Hausdorff space, ISS:X → Y is continuous, injective, and proper, then f is an imbedding and f(X) is closed in Y.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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