Let $X=\{(x,y)\in {\mathbb{R}}^{2}\mid y=0\text{or}x\ge 0\}$ and $f:X\to \mathbb{R}$ defined by $f(x,y)=x$ . I want to find $C\subset X$ closed such that $f(C)\subset \mathbb{R}$ isn't closed. How to prove that f is a closed map?

hornejada1c
2022-07-15
Answered

Let $X=\{(x,y)\in {\mathbb{R}}^{2}\mid y=0\text{or}x\ge 0\}$ and $f:X\to \mathbb{R}$ defined by $f(x,y)=x$ . I want to find $C\subset X$ closed such that $f(C)\subset \mathbb{R}$ isn't closed. How to prove that f is a closed map?

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