CSIR NET MA Solution Dec 2019|Question 69 | Real Analysis | Application | Inverse Mapping | Open Set

CSIR NET Mathematical Science 2019 Solution Series
Question 69
Real Analysis

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CSIR NET MA Solutions
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CSIR NET MA 2019 section A Question 69
real analysis csir net 2019
part C csir net
Application of inverse mapping theorem
image of open set is open
Implicit mapping theorem
AXIOMATIKOS

For queries and suggestion please comment or

[AamirHLone]

Proof of option 1) is superb. Thanks for that!

[AamirHLone]

For option 4) take f: R to R, f(x)= e^-x

[reneemiriam]

Sir, I could not understand option 4 . Can you please help me. You said a space must be both open and closed. I could not understand that because you took ( -1, 0 ) U (0, 1) which is open

[Ramanarajacademy]

If i choose U as (0, 1) then f:U to R is homeomorphism?

[ummeammara]

Sir how f(x)= x^2 is infinitely many times differentiable plss tellll

[AamirHLone]

Ha ha ha
(-1, 0)u(0, 1) is closed! Hu wastage!