Let $K \subset [0,1]$ be the Cantor set. show that $f : [0, 1] \to \mathbb R$...
47016
Riemann integral of characteristic function of Cantor set
119886
The cantor set is uncountable
272
Cantor Sets/nonempty/cardinality
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
49039
Sets with Hausdorff-Measure 0
12402
Showing a function on $[0,1]$ is the zero function
48727
Why is the Cantor set not defined by a limit?
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
38286
Proving the Cantor Pairing Function Bijective
155063
Is Cl(f(A)) a subset of f(Cl(A))?
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
85870
Show this set is a base for some topology on $\mathbb{Z}$
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
104234
What is the Hausdorff dimension of the set of irrationals on $\mathbb R^1$
147350
Homeomorphism between $\prod X_i$ and the Cantor set