real analysis? topology 3. Let ( f: mathbb{R}^{k} rightarrow mathbb{R} ) and ( g: mathbb{R}^{k} rightarrow mathbb{R} ) be continuous functions on ( mathbb{R}^{k} ). a. Prove that the zero set of ( f Z(f):= left {x in mathbb{R}^{k} mid f(x)=0 right } ) is closed. b. Prove that the set ( left {x in mathbb{R}^{k} mid f(x)=g(x) r solutionspile.com

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real analysis? topology 3. Let  ( f:  mathbb{R}^{k}  rightarrow  mathbb{R}  ) and  ( g:  mathbb{R}^{k}  rightarrow  mathbb{R}  ) be continuous functions on  (  mathbb{R}^{k}  ). a. Prove that the zero set of  ( f Z(f):= left {x  in  mathbb{R}^{k}  mid f(x)=0 right }  ) is closed. b. Prove that the set  (  left {x  in  mathbb{R}^{k}  mid f(x)=g(x) right }  ) is closed. c. Prove that the set  (  left {x  in  mathbb{R}^{k}  mid f(x)>g(x) right }  ) is open. solutionspile.com

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(Solved): real analysis topology 3. Let \( f: \mathbb{R}^{k} \rightarrow \mathbb{R} \) and \( g: \mathbb{R} ...

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