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Exercise 2. Let f: X→Y be a map between the topological spaces X and Y. a) Let V V(x) be a neighborhood of x E X. If the restriction f Va Va →Y is continuous at x, show that f: X→Y is continuous at x. b) Assume that (Ui)ier is an open covering of X, show that f: XY is continuous if and only if the restriction f|U₁: U₁Y is continuous, for every i I. 1) T dai CL V Lit hit

Exercise 2. Let f: X→Y be a map between the topological spaces X and Y. a) Let V V(x) be a neighborhood of x E X. If the restriction f Va Va →Y is continuous at x, show that f: X→Y is continuous at x. b) Assume that (Ui)ier is an open covering of X, show that f: XY is continuous if and only if the restriction f|U₁: U₁Y is continuous, for every i I. 1) T dai CL V Lit hit

Advanced Engineering Mathematics
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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Exercise 2 Need part a and part b
that J is automatically continuous! true prove it, II false give an example] Exercise 2. Let f: X→Y be a map between the topological spaces X and Y. a) Let V₂ = V(x) be a neighborhood of x E X. If the restriction f V₂ V₂ →Y is continuous at x, show that f: X→Y is continuous at x. b) Assume that (Ui)ier is an open covering of X, show that f: X→ Y is continuous if and only if the restriction f|U₁ : U₁ → Y is continuous, for every i I. Fuengigo 2 (V Show th TTD shita with Tingghita
Transcribed Image Text:that J is automatically continuous! true prove it, II false give an example] Exercise 2. Let f: X→Y be a map between the topological spaces X and Y. a) Let V₂ = V(x) be a neighborhood of x E X. If the restriction f V₂ V₂ →Y is continuous at x, show that f: X→Y is continuous at x. b) Assume that (Ui)ier is an open covering of X, show that f: X→ Y is continuous if and only if the restriction f|U₁ : U₁ → Y is continuous, for every i I. Fuengigo 2 (V Show th TTD shita with Tingghita
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