Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Set
|
| gptkbp:analyzes |
a series of removed intervals
|
| gptkbp:constructed_in |
intervals
removing middle thirds |
| gptkbp:has_cardinality |
continuum
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor set
|
| gptkbp:introduced_in |
gptkb:Georg_Cantor
|
| gptkbp:is_a |
gptkb:topology
gptkb:Fraggle nowhere dense set closed set set of points self-similar set Lebesgue measurable set closed and bounded set compact set non-empty set perfect set set with empty interior totally disconnected space perfect subset of real numbers set that is a subset of the real line set that is closed in the standard topology set that is compact and perfect set that is nowhere dense in real numbers set that is totally disconnected set that is uncountably infinite set with cardinality of the continuum set with no intervals set with no isolated points set with perfect closure subset of the real line |
| gptkbp:is_characterized_by |
perfect set property
|
| gptkbp:is_closed_under |
complementation
|
| gptkbp:is_connected_to |
gptkb:Cantor_function
|
| gptkbp:is_countable |
no
|
| gptkbp:is_defined_by |
iterative process
|
| gptkbp:is_described_as |
gptkb:topology
|
| gptkbp:is_homeomorphic_to |
gptkb:Cantor_space
|
| gptkbp:is_related_to |
gptkb:analysis
Baire category theorem Cantor's diagonal argument |
| gptkbp:is_subset_of |
real numbers
|
| gptkbp:is_uncountable |
yes
|
| gptkbp:is_used_in |
gptkb:Set
real analysis fractal geometry |
| gptkbp:length |
zero
|
| gptkbp:bfsParent |
gptkb:Christianity
gptkb:Georg_Cantor |
| gptkbp:bfsLayer |
4
|