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(Q4781718)
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English
approach space
set equipped with a point-to-subset distance function
In more languages
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Statements
subclass of
mathematical structure
0 references
studied in
general topology
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metric geometry
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defining formula
d
:
X
×
Pow
(
X
)
→
[
0
,
∞
]
d
(
x
,
{
x
}
)
=
0
d
(
x
,
∅
)
=
∞
d
(
x
,
A
∪
B
)
=
min
{
d
(
x
,
A
)
,
d
(
x
,
B
)
}
∀
ϵ
∈
[
0
,
∞
]
:
d
(
x
,
A
)
≤
d
(
x
,
{
y
∈
X
|
d
(
y
,
A
)
≤
ϵ
}
)
+
ϵ
{\displaystyle {\begin{aligned}d\colon X\times \operatorname {Pow} (X)&\to [0,\infty ]\\d(x,\{x\})&=0\\d(x,\varnothing )&=\infty \\d(x,A\cup B)&=\min\{d(x,A),d(x,B)\}\\\forall \epsilon \in [0,\infty ]\colon d(x,A)&\leq d(x,\{y\in X|d(y,A)\leq \epsilon \})+\epsilon \end{aligned}}}
0 references
in defining formula
(
X
,
d
)
{\displaystyle (X,d)}
symbol represents
approach space
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X
{\displaystyle X}
symbol represents
set
0 references
Pow
{\displaystyle \operatorname {Pow} }
symbol represents
power set
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Identifiers
Freebase ID
/m/05bxp5
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Microsoft Academic ID
2776772326
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nLab ID
approach space
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Sitelinks
Wikipedia
(1 entry)
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enwiki
Approach space
Wikibooks
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Wikinews
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Wikiquote
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Wikisource
(0 entries)
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Wikiversity
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Wikivoyage
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Wiktionary
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Multilingual sites
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![{\displaystyle {\begin{aligned}d\colon X\times \operatorname {Pow} (X)&\to [0,\infty ]\\d(x,\{x\})&=0\\d(x,\varnothing )&=\infty \\d(x,A\cup B)&=\min\{d(x,A),d(x,B)\}\\\forall \epsilon \in [0,\infty ]\colon d(x,A)&\leq d(x,\{y\in X|d(y,A)\leq \epsilon \})+\epsilon \end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cdfee76da27688dd6232f26cf9f700ff961401b)