Any continuous map $f:\mathbb{R}\to\mathbb{Z}$ is constant
727
Prove that any continuous integer-valued function of a real variable is constant.
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
129324
Let $f:[0;1]\to\mathbb R$ be continiously differentiable
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
105700
Proving $\,f$ is constant.
72044
prove $x \mapsto x^2$ is continuous
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
103932
How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?
34344
Is a function that maps every compact set to a compact set continuous?
88586
show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
4538
Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?