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ThmDex – An index of mathematical definitions, results, and conjectures.
Definitions
,
Results
,
Conjectures
▼
Set of symbols
▼
Alphabet
▼
Deduction system
▼
Theory
▼
Zermelo-Fraenkel set theory
▼
Set
▼
Binary cartesian set product
▼
Binary relation
▼
Map
▼
Operation
▼
N-operation
▼
Binary operation
▼
Basic binary operation
▼
Unsigned basic binary operation
▼
Semimetric
▼
Metric
▼
Metric space
▼
Lipschitz map
Definition D48
Bilipschitz map
Formulation 0
Let
M
X
=
(
X
,
d
X
)
and
M
Y
=
(
Y
,
d
Y
)
each be a
D1107: Metric space
.
A
D18: Map
f
:
X
→
Y
is a
bilipschitz map
from
M
X
to
M
Y
if and only if
∃
C
∈
[
1
,
∞
)
:
∀
x
,
y
∈
X
:
1
C
d
X
(
x
,
y
)
≤
d
Y
(
f
(
x
)
,
f
(
y
)
)
≤
C
d
X
(
x
,
y
)
Results
▶
R81: Bilipschitz map is continuous