Statements (38)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:constructed_in |
iterative process
|
| gptkbp:defined_on |
gptkb:Cantor_set
|
| gptkbp:example |
a function that is continuous everywhere but differentiable nowhere
a singular function a function that is continuous but not absolutely continuous a function with a jump discontinuity a function with zero derivative almost everywhere |
| gptkbp:has_derivative |
0 almost everywhere
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor function
|
| gptkbp:is_constant_on |
(1/3, 2/3)
|
| gptkbp:is_continuous |
gptkb:true
|
| gptkbp:is_defined_by |
the intervals removed in the construction of the Cantor set
the construction of the Cantor set the mapping of intervals to points in [0, 1] the sum of the lengths of the removed intervals |
| gptkbp:is_graph_of |
a continuous function
a non-linear function |
| gptkbp:is_monotonic |
gptkb:true
|
| gptkbp:is_non_decreasing |
gptkb:true
|
| gptkbp:is_not_differentiable |
at points of the Cantor set
|
| gptkbp:is_not_injective |
gptkb:true
|
| gptkbp:is_not_linear |
gptkb:true
|
| gptkbp:is_not_surjective |
gptkb:true
|
| gptkbp:is_related_to |
gptkb:Cantor_set
gptkb:Lebesgue_measure Baire category theorem Cantor ternary set measure zero sets |
| gptkbp:is_used_in |
gptkb:topology
gptkb:analysis real analysis fractal geometry |
| gptkbp:known_as |
Devil's staircase
|
| gptkbp:map |
[0, 1]
|
| gptkbp:range |
[0, 1]
|
| gptkbp:bfsParent |
gptkb:Cantor_set
|
| gptkbp:bfsLayer |
5
|