query: Every continuous function on Q can be extended to R continuously. ls it true or false?
positive_passages.docid: 24914
positive_passages.text: Does every continuous map from $\mathbb{Q}$ to $\mathbb{Q}$ extends continuously as a map from $\mathbb{R}$ to $\mathbb{R}$?
negative_passages.docid: 53841
negative_passages.text: Function always continuous in a Sobolev Space?
negative_passages.docid: 102075
negative_passages.text: A function continuous on all irrational points
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 29180
negative_passages.text: If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
negative_passages.docid: 34344
negative_passages.text: Is a function that maps every compact set to a compact set continuous?
negative_passages.docid: 143695
negative_passages.text: Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
negative_passages.docid: 44574
negative_passages.text: Continuity of absolute value of a function
negative_passages.docid: 93021
negative_passages.text: $f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
negative_passages.docid: 143618
negative_passages.text: If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 30590
negative_passages.text: Are "most" continuous functions also differentiable?
negative_passages.docid: 155618
negative_passages.text: Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
negative_passages.docid: 115930
negative_passages.text: Is every convex function on an open interval continuous?
negative_passages.docid: 128911
negative_passages.text: Continuous extension of a real function