query: Additive function $f:\mathbb R\to \mathbb R$ that is not continuous.
positive_passages.docid: 5373
positive_passages.text: Additive function $T: \mathbb{R} \rightarrow \mathbb{R}$ that is not linear.
negative_passages.docid: 30036
negative_passages.text: Function in $H^1$, but not continuous
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 52922
negative_passages.text: let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
negative_passages.docid: 40576
negative_passages.text: Intermediate value property problem and continuous function
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 137815
negative_passages.text: Additive but not $\sigma$-additive function
negative_passages.docid: 11828
negative_passages.text: continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
negative_passages.docid: 52798
negative_passages.text: Finding counterexamples: bijective continuous functions that are not homeomorphisms
negative_passages.docid: 121957
negative_passages.text: Is $p\mapsto \|f\|_p$ continuous?
negative_passages.docid: 68165
negative_passages.text: Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
negative_passages.docid: 37966
negative_passages.text: If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
negative_passages.docid: 88240
negative_passages.text: Two functions discontinuous, but sum continuous
negative_passages.docid: 9406
negative_passages.text: Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
negative_passages.docid: 124535
negative_passages.text: continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
negative_passages.docid: 3518
negative_passages.text: Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous