query: The composition of continuous functions on $\mathbb{R}$ is continuous
positive_passages.docid: 71487
positive_passages.text: Real Analysis: Continuity of a Composition Function
negative_passages.docid: 98772
negative_passages.text: Continuity of a function in $\mathbb{R}$
negative_passages.docid: 115794
negative_passages.text: When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
negative_passages.docid: 121957
negative_passages.text: Is $p\mapsto \|f\|_p$ continuous?
negative_passages.docid: 108115
negative_passages.text: If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
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: 100740
negative_passages.text: proof of that a continuous function has a fixed point
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 47419
negative_passages.text: Asymptotics of uniformly continuous functions over $\mathbb R$
negative_passages.docid: 69869
negative_passages.text: if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
negative_passages.docid: 124535
negative_passages.text: continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
negative_passages.docid: 14495
negative_passages.text: I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
negative_passages.docid: 130023
negative_passages.text: Prove that the sum of two continuous functions is continuous
negative_passages.docid: 55605
negative_passages.text: If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
negative_passages.docid: 36149
negative_passages.text: A uniformly continuous function maps bounded set to bounded sets
negative_passages.docid: 33330
negative_passages.text: Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$