10* Suppose ECR is separated by a pair of relative open subsets U, V Define a function on E as following: f(x)=(-1, x EV EU Show that is continuous on E; that is, for any a € E, given any > 0, there is 8 >0 such that x € (a-8,a+8) nElf(x)-f(a)|
10* Suppose ECR is separated by a pair of relative open subsets U, V Define a function on E as following: f(x)=(-1, x EV EU Show that is continuous on E; that is, for any a € E, given any > 0, there is 8 >0 such that x € (a-8,a+8) nElf(x)-f(a)|
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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please write down your answer in detail.
![10* Suppose ECR is separated
by a pair of relative open subsets U, V Define a function on E as
following: f(x) =
(1, X EU
-1, x EV
Show that is continuous on E; that is, for any a E E, given any >
0, there is 8 >0 such that x E (a-8, a +8) nElf(x)-f(a)| <e. Hint: Apply 8.27 Remark.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dad2b96-f364-4363-a6d8-0a1d6331f902%2F8a6f65bc-593b-45bd-95ae-3b82661edcee%2Feedrej6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10* Suppose ECR is separated
by a pair of relative open subsets U, V Define a function on E as
following: f(x) =
(1, X EU
-1, x EV
Show that is continuous on E; that is, for any a E E, given any >
0, there is 8 >0 such that x E (a-8, a +8) nElf(x)-f(a)| <e. Hint: Apply 8.27 Remark.
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