the middle-thirds Cantor set
GPTKB entity
Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:topology
fractal mathematical set |
| gptkbp:builtBy |
removing the open middle third of each interval at each step
|
| gptkbp:cardinality |
uncountable
|
| gptkbp:compact |
true
|
| gptkbp:contains |
0
1 all points in [0,1] with ternary expansions using only 0 and 2 |
| gptkbp:firstDescribed |
1883
|
| gptkbp:hasInvariant |
scaling by 1/3
|
| gptkbp:hasSubgroup |
[0,1]
|
| gptkbp:HausdorffDimension |
log(2)/log(3)
|
| https://www.w3.org/2000/01/rdf-schema#label |
the middle-thirds Cantor set
|
| gptkbp:isClosed |
true
|
| gptkbp:isNowhereDense |
true
|
| gptkbp:isomorphicTo |
the product of countably infinite copies of the discrete space {0,1}
|
| gptkbp:isPerfect |
true
|
| gptkbp:isSelfSimilar |
true
|
| gptkbp:isTotallyDisconnected |
true
|
| gptkbp:isUniversal |
for compact, perfect, totally disconnected metric spaces
|
| gptkbp:measures |
0
|
| gptkbp:namedAfter |
gptkb:Georg_Cantor
|
| gptkbp:topologicalDimension |
0
|
| gptkbp:usedIn |
gptkb:topology
measure theory real analysis fractal geometry |
| gptkbp:bfsParent |
gptkb:Cantor_space
|
| gptkbp:bfsLayer |
8
|