What is a continuous function on the rationals that hasn't a continuous extension on the reals?
24914
Does every continuous map from $\mathbb{Q}$ to $\mathbb{Q}$ extends continuously as a map from $\mathbb{R}$ to $\mathbb{R}$?
121957
Is $p\mapsto \|f\|_p$ continuous?
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
146707
Formally show that the set of continuous functions is not measurable
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
22641
Nonlinear function continuous but not bounded
55243
When is the ring of continuous functions Noetherian?
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
120947
continuous real-valued function
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
143798
Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.
158567
A uniform continuous function which is not Hölder continuous
3801
Functions that take rationals to rationals
32205
Topology on the real numbers such that all polynomials are continuous but cosine is not continuous
94109
$f$ a real, continuous function, is it measurable?