If $f:[0,1]\to (0,1)$ is a continuous mapping then which are NOT correct?
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
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$[0,1]$
34344
Is a function that maps every compact set to a compact set continuous?
100465
Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
122086
continuous function: preimage of closure of a set is closure of preimage
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
158344
Uniform continuous maps that converge uniformly to a function f. What can we say about f?
38584
$T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.
116732
Proving that a continuous map is surjective
153495
Continuous function does not map closed set to closed set
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.