Is there a function $f:\mathbb{R} \to \mathbb{R}$ such that a set of all continuous points of $f$ is "given" $G_\delta$ set?
18222
Set of continuity points of a real function
41690
Products of Continuous functions: Topology
34836
Composition of Absolutely Continuous Functions
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
32571
Is the maximum function of a continuous function continuous?
43189
Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
23728
Does a continuous and 1-1 function map Borel sets to Borel sets?
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
55679
Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
77323
Existence of continuous angle function $\theta:S^1\to\mathbb{R}$
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
10747
Given function $g$ continuous in line $[0,\infty)$...
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
103241
A function that is continuous at the origin but not differentiable there