Is the function from $\mathbb{R}$ to $\mathbb{R}$ that maps every compact set to compact set and connected set to connected set continuous?

Asked Jan 04 '17 at 09:22

Active Jan 04 '17 at 09:35

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Is the function from $\mathbb{R}$ to $\mathbb{R}$ that maps every compact set to compact set and connected set to connected set continious?

I know that if the function maps only compact set (respectively connected) to compact (connected) it's not continious. I saw the counterexample. Is it also true when we take both properties?

Thanks in advance.

edited Jan 04 '17 at 09:35

asked Jan 04 '17 at 09:22

user224301

Are you talking about functions from $\mathbb R$ to $\mathbb R,$ or functions from a general topological space to a general topological space, or what? – bof Jan 04 '17 at 09:27
1

Ok. Jimmy R. gave counterexample for general topological spaces. So how is it with function $\mathbb{R}$ to $\mathbb{R}$? – user224301 Jan 04 '17 at 09:29
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See this. – David Mitra Jan 04 '17 at 09:39
Ok. I suck in finding stuff. Thanks. That is the awnser for my question. – user224301 Jan 04 '17 at 09:43

Is the function from $\mathbb{R}$ to $\mathbb{R}$ that maps every compact set to compact set and connected set to connected set continuous?

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