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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2F997b26e8-7a3d-4b09-ab3a-b998b832389d%2Fjm13w0p_processed.jpeg&w=3840&q=75)
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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