Rationals can be the set of continuity of a function?
18222
Set of continuity points of a real function
15914
Prove that any polynomial function is continuous
24817
Prove continuity on a function at every irrational point and discontinuity at every rational point.
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
40349
Continuity of analytic function implies convergence of power series?
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
154572
Continuity of a function at an isolated point
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
57233
Proof of continuity of Thomae Function at irrationals.
12523
Supremum of a Continuous Function is Continuous
83204
Is every $G_\delta$ set the set of continuity points of some function $f$?
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
95294
Dense subset of $C[0,1]$ which preserves rationals