the middle-thirds Cantor set

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:topology gptkb:fractal gptkb: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)
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
https://www.w3.org/2000/01/rdf-schema#label	the middle-thirds Cantor set