#2 Given A C R" and f : A → R", define I; = {(x, f(x)) E R" × R" | x € A}. The following questions are independent. (a) If is closed in Rm × R". Suppose A is closed and that f is continuous on A (relative to A). Prove that (b) that I; is connected. (First prove that F: A → R" × R² given by F(x) = (x, f (x)) is continuous on A relative to A.) Suppose A is connected and that f is continuous on A (relative to A). Prove
#2 Given A C R" and f : A → R", define I; = {(x, f(x)) E R" × R" | x € A}. The following questions are independent. (a) If is closed in Rm × R". Suppose A is closed and that f is continuous on A (relative to A). Prove that (b) that I; is connected. (First prove that F: A → R" × R² given by F(x) = (x, f (x)) is continuous on A relative to A.) Suppose A is connected and that f is continuous on A (relative to A). Prove
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve (b)
Transcribed Image Text:#2 Given A C R" and f : A → R", define
Tf = {(x, f(x)) E R™ × R" | x E A}.
The following questions are independent.
(a)
Tf is closed in Rm × R".
Suppose A is closed and that f is continuous on A (relative to A). Prove that
(b)
that I; is connected. (First prove that F : A → R" × R" given by F(x) = (x, f (x)) is
continuous on A relative to A.)
Suppose A is connected and that f is continuous on A (relative to A). Prove
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