query: Example of a function ($\mathbb{R}$ to $\mathbb{R}$) which is continuous only at two point .
positive_passages.docid: 26955
positive_passages.text: Continuous at exactly two points and differentiable at exactly one of them
negative_passages.docid: 50111
negative_passages.text: non-continuous function satisfies $f(x+y)=f(x)+f(y)$
negative_passages.docid: 130019
negative_passages.text: Function that is continuous only on the transcendental numbers
negative_passages.docid: 63598
negative_passages.text: Is every separately continuous function on $R^2$ continuous?
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 113498
negative_passages.text: Example of topological spaces where sequential continuity does not imply continuity
negative_passages.docid: 41201
negative_passages.text: How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
negative_passages.docid: 22641
negative_passages.text: Nonlinear function continuous but not bounded
negative_passages.docid: 14578
negative_passages.text: Proving that an additive function $f$ is continuous if it is continuous at a single point
negative_passages.docid: 7036
negative_passages.text: Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
negative_passages.docid: 95970
negative_passages.text: Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
negative_passages.docid: 141223
negative_passages.text: $f(x^2) = 2f(x)$ and $f(x)$ continuous
negative_passages.docid: 91852
negative_passages.text: A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
negative_passages.docid: 52922
negative_passages.text: let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
negative_passages.docid: 19916
negative_passages.text: $f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
negative_passages.docid: 73585
negative_passages.text: Why is the function continuous, if it is defined only on integers?
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions