Prove there is no bijective continuous function $f:[0,1] \to [0,1]^2$
106884
Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?
10307
Show the inverse of a bijective function is bijective
146055
Proving a set of functions is uncountable
143798
Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
72115
Why isn't there a continuously differentiable surjection from $I \to I \times I$?
153495
Continuous function does not map closed set to closed set
64866
Proving a Composition of Functions is Bijective
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$