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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
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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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.
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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