Example of function $f:\Bbb R\to \Bbb R$ continuous at $x$ iff $x$ is trascendental
130019
Function that is continuous only on the transcendental numbers
98772
Continuity of a function in $\mathbb{R}$
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
148328
Example of a function $f$ on $X$ to $\mathbb{R}$ which is not $X$-measurable but $|f|$, and $f^2$ are measurable.
53627
Proving continuity of $f$
154572
Continuity of a function at an isolated point
59519
What about the continuity of these functions in the uniform topology?
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
97619
Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
62817
Functions which are Continuous, but not Bicontinuous
118192
Is there a bijective function $f: \mathbb{R}\to\mathbb{R}$ that is discontinuous?
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
153406
$[F(t):F(t^n)]=n$ where $t$ is trascendental
28111
Let $f:[1,10]\to \Bbb{Q}$ be a continuous function and $f(1)=10,$then $f(10)=?$
86327
If the absolute value of a function is continuous, is the function continuous?