query: Continuity of Function $f:R-R$
positive_passages.docid: 149095
positive_passages.text: $f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
negative_passages.docid: 158567
negative_passages.text: A uniform continuous function which is not Hölder continuous
negative_passages.docid: 73594
negative_passages.text: Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
negative_passages.docid: 40209
negative_passages.text: $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
negative_passages.docid: 155923
negative_passages.text: continuity of $f(x,y)$ in $\mathbb R^2$.
negative_passages.docid: 118332
negative_passages.text: proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
negative_passages.docid: 154572
negative_passages.text: Continuity of a function at an isolated point
negative_passages.docid: 80643
negative_passages.text: Show that f(x) defined on [0,infinity) R to is continuous at 0.
negative_passages.docid: 132013
negative_passages.text: How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
negative_passages.docid: 46642
negative_passages.text: Continuity of $\sin(x)/x$
negative_passages.docid: 15579
negative_passages.text: Show that $f$ is uniformly continuous if limit exists
negative_passages.docid: 105652
negative_passages.text: Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
negative_passages.docid: 124779
negative_passages.text: Intuition for uniform continuity of a function on $\mathbb{R}$
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 9320
negative_passages.text: Extension of continuous function on a closed subset of $\mathbb{R}$
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 81223
negative_passages.text: Real Analysis Question: continuity of $f(x) = \sum_{q_n<x} 1/n^2$