Question

The Cantor set is uncountable even though it is a closed set with outer meaure $0.$ ("Measure, Integration & Real Analysis" by Sheldon Axler. )

score 74 · Answer 1 · 2023-04-18 05:29:47

74

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The Cantor set is uncountable even though it is a closed set with outer meaure $0.$ ("Measure, Integration & Real Analysis" by Sheldon Axler. )

Published on 18 Apr 2023 - 5:29

score 225 · Answer 2 · 2023-04-25 15:33:39

225

Views

Constructing a Homeomorphism with the Cantor Set

Published on 25 Apr 2023 - 15:33

score 53 · Answer 3 · 2023-04-26 00:05:27

53

Views

Is the collapsed Cantor set homeomorphic to the interval $[0,1]$?

Published on 26 Apr 2023 - 0:05

score 49 · Answer 4 · 2023-05-05 05:57:30

49

Views

An increasing, continuous function $f$ such that $f'=0$ a.e. outside an arbitrary exceptional uncountable set with measure 0.

Published on 05 May 2023 - 5:57

score 143 · Answer 5 · 2023-05-08 03:53:32

143

Views

Prove that union of intersections of nested balls in $R^k$ is a perfect set

Published on 08 May 2023 - 3:53

score 52 · Answer 6 · 2023-05-25 15:40:43

52

Views

Does this work to prove that the cantor set lacks isolated points?

Published on 25 May 2023 - 15:40

score 66 · Answer 7 · 2023-06-09 17:26:50

66

Views

Self-homeomorphisms of the Cantor set

Published on 09 Jun 2023 - 17:26

score 88 · Answer 8 · 2023-06-24 18:17:55

88

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Bijection between Cantor set and binary sequences; Hunter

Published on 24 Jun 2023 - 18:17

score 62 · Answer 9 · 2023-07-07 18:46:03

62

Views

Does anyone have a nicer closed formula for the Cantor function?

Published on 07 Jul 2023 - 18:46

score 28 · Answer 10 · 2023-07-12 12:59:23

28

Views

To prove that the Cantor function maps the end points of the intervals removed to a same point

Published on 12 Jul 2023 - 12:59

score 229 · Answer 11 · 2023-07-17 14:34:13

229

Views

Has this "thinner" Cantor set been defined and studied before?

Published on 17 Jul 2023 - 14:34

score 41 · Answer 12 · 2023-07-17 14:54:36

41

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An exercise about the Cantor measure

Published on 17 Jul 2023 - 14:54

score 94 · Answer 13 · 2026-02-24 03:04:54

94

Views

Determining whether a natural number has no "1"s in its ternary expansion, without direct calculation

Published on 24 Feb 2026 - 3:04

score 50 · Answer 14 · 2023-07-28 20:58:35

50

Views

Properties of Cantor-like function

Published on 28 Jul 2023 - 20:58

score 70 · Answer 15 · 2023-08-04 15:28:26

70

Views

How many "disconnections" are there in the Cantor set?

Published on 04 Aug 2023 - 15:28

List Question

The Cantor set is uncountable even though it is a closed set with outer meaure $0.$ ("Measure, Integration & Real Analysis" by Sheldon Axler. )

Constructing a Homeomorphism with the Cantor Set

Is the collapsed Cantor set homeomorphic to the interval $[0,1]$?

An increasing, continuous function $f$ such that $f'=0$ a.e. outside an arbitrary exceptional uncountable set with measure 0.

Prove that union of intersections of nested balls in $R^k$ is a perfect set

Does this work to prove that the cantor set lacks isolated points?

Self-homeomorphisms of the Cantor set

Bijection between Cantor set and binary sequences; Hunter

Does anyone have a nicer closed formula for the Cantor function?

To prove that the Cantor function maps the end points of the intervals removed to a same point

Has this "thinner" Cantor set been defined and studied before?

An exercise about the Cantor measure

Determining whether a natural number has no "1"s in its ternary expansion, without direct calculation

Properties of Cantor-like function

How many "disconnections" are there in the Cantor set?

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