Question

Is it true that if $A$ and $B$ are nowhere dense subsets of $[0,1]$ then the Minkowski sum $A+B=\{a+b:\ a\in A, b\in B\}$ is nowhere dense in $[0,2]$?

score 133 · Answer 1 · 2021-09-11 13:13:12

133

Views

Is it true that if $A$ and $B$ are nowhere dense subsets of $[0,1]$ then the Minkowski sum $A+B=\{a+b:\ a\in A, b\in B\}$ is nowhere dense in $[0,2]$?

Published on 11 Sep 2021 - 13:13

score 171 · Answer 2 · 2021-09-17 22:18:30

171

Views

Is the Cantor set $\mathcal{C} = \bigcap_{k=0}^{\infty} C_k$ the set of all the endpoints of the closed intervals of the $C_k$'s?

Published on 17 Sep 2021 - 22:18

score 190 · Answer 3 · 2021-09-20 10:02:15

190

Views

Cantor space has a binary tree structure?

Published on 20 Sep 2021 - 10:02

score 392 · Answer 4 · 2021-09-28 20:35:01

392

Views

Two equivalent definitions of the Cantor function

Published on 28 Sep 2021 - 20:35

score 757 · Answer 5 · 2021-10-02 13:45:07

757

Views

Every open interval of $\mathbb{R}$ contains either infinitely many or no elements in the Cantor set

Published on 02 Oct 2021 - 13:45

score 405 · Answer 6 · 2021-10-05 09:08:32

405

Views

Properties of fat Cantor set

Published on 05 Oct 2021 - 9:08

score 151 · Answer 7 · 2021-10-06 22:14:10

151

Views

Evaluating the integral of the Cantor function

Published on 06 Oct 2021 - 22:14

score 175 · Answer 8 · 2021-10-19 17:38:05

175

Views

Cantor function integral.

Published on 19 Oct 2021 - 17:38

score 101 · Answer 9 · 2021-11-02 20:43:26

101

Views

How than I show that this map is continuous?

Published on 02 Nov 2021 - 20:43

score 149 · Answer 10 · 2021-11-21 17:16:27

149

Views

Bound on variation $|F(x)-F(y)|$ where $F$ is Cantor's function

Published on 21 Nov 2021 - 17:16

score 49 · Answer 11 · 2021-11-25 00:40:25

49

Views

Cantor function satisfies for $x\in[{0,{1\over 3}]}$ $F(x)={1\over 2}{F(2x)}$

Published on 25 Nov 2021 - 0:40

score 170 · Answer 12 · 2021-12-04 11:05:40

170

Views

Need clarification on definition of cantor distribution

Published on 04 Dec 2021 - 11:05

score 465 · Answer 13 · 2021-12-22 23:11:38

465

Views

Ring homomorphisms between $C([0,1], \mathbb{R})$ and $C(\text{Cantor set},\mathbb{R})$

Published on 22 Dec 2021 - 23:11

score 76 · Answer 14 · 2021-12-27 15:25:03

76

Views

Constructive proof of representation for open balls in Cantor space

Published on 27 Dec 2021 - 15:25

score 230 · Answer 15 · 2021-12-29 02:44:51

Does there exist any continuous function $f:\mathbb{R} \to \mathbb{R}$ such that $f(\mathbb{R}\setminus \mathbb{Q}) = \mathbb{R}$?

List Question

Is it true that if $A$ and $B$ are nowhere dense subsets of $[0,1]$ then the Minkowski sum $A+B=\{a+b:\ a\in A, b\in B\}$ is nowhere dense in $[0,2]$?

Is the Cantor set $\mathcal{C} = \bigcap_{k=0}^{\infty} C_k$ the set of all the endpoints of the closed intervals of the $C_k$'s?

Cantor space has a binary tree structure?

Two equivalent definitions of the Cantor function

Every open interval of $\mathbb{R}$ contains either infinitely many or no elements in the Cantor set

Properties of fat Cantor set

Evaluating the integral of the Cantor function

Cantor function integral.

How than I show that this map is continuous?

Bound on variation $|F(x)-F(y)|$ where $F$ is Cantor's function

Cantor function satisfies for $x\in[{0,{1\over 3}]}$ $F(x)={1\over 2}{F(2x)}$

Need clarification on definition of cantor distribution

Ring homomorphisms between $C([0,1], \mathbb{R})$ and $C(\text{Cantor set},\mathbb{R})$

Constructive proof of representation for open balls in Cantor space

Does there exist any continuous function $f:\mathbb{R} \to \mathbb{R}$ such that $f(\mathbb{R}\setminus \mathbb{Q}) = \mathbb{R}$?

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