Continuous function which maps (0,1] to {0}, (0,1), [0,1), [0,1]
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
120947
continuous real-valued function
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
32340
Continuous bijections and their inverses
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
70645
Borel set preserved by continuous map
54797
Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$
45606
Is there a bijection from [0,1] to R?
146306
A continuous surjective function from $(0,1]$ onto $[0,1]$
65472
From injective map to continuous map
3276
Function $f:[0,1] \to [0,1]$ taking on each value in $[0,1]$ exactly twice
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
128911
Continuous extension of a real function
111477
Specify a bijection from [0,1] to (0,1].