4. Suppose i: (X.T) (X,S) is the identity function; that is, i(z) = z for every z E X. Prove that i is continuous if and only if SCT.
4. Suppose i: (X.T) (X,S) is the identity function; that is, i(z) = z for every z E X. Prove that i is continuous if and only if SCT.
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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Transcribed Image Text:is an element B of B such that z € B and ƒ(B) C C.
4. Suppose i: (X.T)
(X.S) is the identity function; that is, i(z) = z for
every z E X. Prove that i is continuous if and only if S CT.
TY
**
IV
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