Continuous function which has only rational values.
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
3801
Functions that take rationals to rationals
79107
Give an example of a function $f: \mathbb{R} \to \mathbb{R}$ which is continuous only at $0$.
234
No continuous function switches $\mathbb{Q}$ and the irrationals
139763
A function takes every function value twice - proof it is not continuous
82280
Problem about continuous functions and the intermediate value theorem
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
71487
Real Analysis: Continuity of a Composition Function
99179
Continuous function with compact domain has continuous inverse
119060
What can you say about a continuous function that is zero at all integer values?
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
32571
Is the maximum function of a continuous function continuous?
12523
Supremum of a Continuous Function is Continuous
18222
Set of continuity points of a real function
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
727
Prove that any continuous integer-valued function of a real variable is constant.