다양체,manifold

Difference between r1.4 and the current

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위상다양체
<<tableofcontents>>
= Sub =
== topological m. ==
위상다양체 topological_manifold
WtEn:topological_manifold
https://mathworld.wolfram.com/TopologicalManifold.html
https://www.proofwiki.org/wiki/Definition:Topological_Manifold
WpEn:Topological_manifold 
= https://en.wikipedia.org/wiki/Topological_manifold
WpSp:topological_manifold jjjjjjjjjjj
[[WpEn:Topological_manifold]] = https://en.wikipedia.org/wiki/Topological_manifold
https://ncatlab.org/nlab/show/topological+manifold
미분다양체
...
Ndict:topological+manifold
Ggl:topological+manifold
topological+manifold
 
== differentiable m. = smooth m. ==
미분다양체 differentiable_manifold = 매끄러운다양체 smooth_manifold
https://mathworld.wolfram.com/SmoothManifold.html
https://freshrimpsushi.github.io/posts/differentiable-manifold/
...
Ndict:미분다양체
Bing:미분다양체
KmsK:미분다양체
Ggl:미분다양체
WpKo:미분다양체
 
Naver:매끄러운다양체
 
== complex m. ==
복소다양체 complex_manifold
[[complex_manifold]] =,complex_manifold =,complex_manifold . complex_manifold
WtEn:complex_manifold
MKLINK: complex_structure { https://ncatlab.org/nlab/show/complex+structure }
WpKo:복소다양체
= https://ko.wikipedia.org/wiki/복소다양체
WpSp:complex_manifold eeeeeeeeeeee
WpEn:Complex_manifold
= https://en.wikipedia.org/wiki/Complex_manifold
https://www.proofwiki.org/wiki/Definition:Topological_Manifold/Complex_Manifold
=== almost complex m. ===
almost complex manifold
almost_complex_manifold
MKLINK: almost_complex_structure or almost-complex_structure { https://encyclopediaofmath.org/wiki/Almost-complex_structure }
https://ko.wikipedia.org/wiki/개복소다양체
https://en.wikipedia.org/wiki/Almost_complex_manifold
Up: 매끄러운다양체
== symplectic m. ==
(tmp) WtEn:symplectic KmsE:symplectic NdEn:symplectic Bing:symplectic Ggl:symplectic
[[symplectic]] =,symplectic .
사교다양체 symplectic_manifold
[[symplectic_manifold]] =,symplectic_manifold =,symplectic_manifold . symplectic_manifold
WtEn:symplectic_manifold
심플렉틱 다양체, 사교다양체
MKLINK: [[symplectic_structure]] [[symplectic_form]]
https://encyclopediaofmath.org/wiki/Symplectic_manifold
https://mathworld.wolfram.com/SymplecticManifold.html
WpKo:심플렉틱_다양체
https://ncatlab.org/nlab/show/symplectic+manifold
 
MKL
[[symplectic_geometry]]
 
== smooth m. / differentiable m. (DUPLICATED; 저위로 MERGE) ==
매끄러운다양체 smooth_manifold
WpKo:매끄러운_다양체
https://mathworld.wolfram.com/SmoothManifold.html
https://www.proofwiki.org/wiki/Definition:Topological_Manifold/Smooth_Manifold
https://ncatlab.org/nlab/show/smooth+manifold
미분가능다양체 differentiable_manifold
[[매끄러움,smoothness]]
미분가능다양체 differentiable_manifold =,differentiable_manifold =,differentiable_manifold . differentiable_manifold
WtEn:differentiable_manifold
https://www.proofwiki.org/wiki/Definition:Differentiable_Manifold
WpEn:Differentiable_manifold 
= https://en.wikipedia.org/wiki/Differentiable_manifold
WpSp:differentiable_manifold gggggg
[[WpEn:Differentiable_manifold]] = https://en.wikipedia.org/wiki/Differentiable_manifold
[[미분가능성,differentiability]]
Kähler_manifold /// https://ko.wiktionary.org/wiki/ä https://ko.wikipedia.org/wiki/움라우트 - 그럼 ae로 표현?
== Kähler m. ==
Kähler
Ggl:Kähler
Naver:Kähler
Kähler_manifold 
WtKo:ä = https://ko.wiktionary.org/wiki/ä 
WtEn:ä
https://ko.wikipedia.org/wiki/움라우트 - 그럼 ae로 표현?
Kahler_manifold or
Kaehler_manifold - pagename TBD.
Kaehler_manifold - pagename TBD. WtEn:ä Ndict:ä Naver:ä Bing:ä Ggl:ä Ggl:ä+transliteration Naver:ä+표기 Ggl:ä+표기
[[WpEn:Kähler_manifold]]
= https://en.wikipedia.org/wiki/Kähler_manifold

== m. learning ==
다양체학습? [[학습,learning]]
[[manifold_learning]]
[[manifold_learning]] =,manifold_learning =,manifold_learning . manifold_learning
{
... Google:manifold+learning
 
WtEn:manifold_learning
 
WpSp:manifold_learning eeeeeee
 
WpEn:manifold_learning ffffffff
 
... 
Naver:"manifold learning"
Google:"manifold learning"
YouTube:"manifold learning"
"manifold learning"
manifold+learning
}

MKLINK
symplectic_geometry
https://en.wikipedia.org/wiki/Symplectic_geometry  
[[단위원판,unit_disk]]
= MKLINK =
[[differential_geometry]]
[[symplectic_geometry]] =,symplectic_geometry =,symplectic_geometry . symplectic_geometry
{
WpEn:Unit_disk
= https://en.wikipedia.org/wiki/Unit_disk
WtEn:symplectic_geometry
WpSp:symplectic_geometry iiiiii
https://en.wikipedia.org/wiki/Symplectic_geometry
}
[[열린단위원판,open_unit_disk]]
[[단위원판,unit_disk]] =단위원판,unit_disk =,unit_disk 단위원판 unit_disk
{
WtEn:unit_disk
WpSp:Unit_disk
[[WpEn:Unit_disk]] = https://en.wikipedia.org/wiki/Unit_disk
 
[[단위,unit]] [[원판,disk]]
... Namu:단위원판 Libre:단위원판 Ndict:단위원판 Ggl:단위원판 Bing:단위원판
}
[[열린단위원판,open_unit_disk]] =열린단위원판,open_unit_disk =,open_unit_disk 열린단위원판 open_unit_disk
{
WtEn:open_unit_disk
WpEn:open_unit_disk

----
같은 한국어 단어, 다른 영어 단어:
Ndict:열린단위원판 Naver:열린단위원판 Bing:열린단위원판 Ggl:열린단위원판
}
 
'''manifold'''는 shape의 [[일반화,generalization]]?
shape에 대한 페이지를 만들어야 하는데... or figure?
[[모양,shape]] or [[도형,shape]] or [[도형,geometric_shape]] - 도형이 좀더 기하적인 용어
{
Namu:도형
}
 
'''다양체,manifold''' [[개념,concept]]은
[[곡면,surface]]이나 [[공간,space]] 개념의 [[일반화,generalization]]? [* https://youtu.be/62WNNkoRCLE?si=cUKHk5Ls6SMu_C_E&t=33]
 
= Bmks =
== The Bright Side of Mathematics (YouTube) ==
https://www.youtube.com/@brightsideofmaths
 
Manifolds (Playlist)
https://www.youtube.com/playlist?list=PLBh2i93oe2qvRGAtgkTszX7szZDVd6jh1
[[Date(2023-09-13T14:12:06)]] 현재 Part 20까지 있고 '사용할 수 없는 동영상 5개가 숨겨졌습니다.' + 마지막 Part 20만 dark version 있음, 8일 전. - dark version 만드는 중?
=== 1 ===
Manifolds - Part 1 - Introduction and Topology - YouTube
https://www.youtube.com/watch?v=62WNNkoRCLE&ab_channel=TheBrightSideofMathematics
 
rel
[[위상,topology]] [[위상수학,topology]]
 
== the Manifold Atlas Project ==
Manifold Atlas
http://www.map.mpim-bonn.mpg.de/Main_Page
 
= 같은단어 =
== 같은 한국어 단어, 다른 영어 단어: ==
[[다양체,variety]]
== manifold ==
see [[매니폴드,manifold]]

----
Namu:다양체
= Twins: =
https://artofproblemsolving.com/wiki/index.php/Manifold
https://mathworld.wolfram.com/Manifold.html
WpEn:Manifold
= https://en.wikipedia.org/wiki/Manifold
[[WpSp:Manifold]] = https://simple.wikipedia.org/wiki/Manifold
[[WpEn:Manifold]] = https://en.wikipedia.org/wiki/Manifold
https://www.proofwiki.org/wiki/Definition:Manifold
[[Namu:다양체]] = https://namu.wiki/w/다양체

... Ndict:manifold
... 
Ndict:다양체 (한글검색결과에선 [[다양체,variety]] 내용을 구분할 것..)
Ndict:manifold 
 
Naver:다양체+manifold
 
Bing:다양체+manifold
 
Ggl:다양체+manifold
 
YouTube:다양체+manifold
 
----
cp from local at [[Date(2023-09-24T19:58:36)]]
[[WpKo:다양체]] = https://ko.wikipedia.org/wiki/다양체
[[WpSp:Manifold]] = https://simple.wikipedia.org/wiki/Manifold
[[WpEn:Manifold]]
https://mathworld.wolfram.com/Manifold.html
https://ncatlab.org/nlab/show/manifold
https://encyclopediaofmath.org/wiki/Manifold
[[Libre:다양체]] = https://librewiki.net/wiki/다양체 //// 2022-2 현재토막글 / 2023-09 현재도
https://everything2.com/title/manifold
https://planetmath.org/manifold
 
 
----


[edit]

1. Sub

[edit]

1.1. topological m.

[edit]

1.2. differentiable m. = smooth m.

[edit]

1.3. complex m.

[edit]

1.3.1. almost complex m.

almost complex manifold
almost_complex_manifold
MKLINK: almost_complex_structure or almost-complex_structure { https://encyclopediaofmath.org/wiki/Almost-complex_structure }
https://ko.wikipedia.org/wiki/개복소다양체
https://en.wikipedia.org/wiki/Almost_complex_manifold
Up: 매끄러운다양체
[edit]

1.4. symplectic m.

[edit]

1.5. smooth m. / differentiable m. (DUPLICATED; 저위로 MERGE)

[edit]

1.6. Kähler m.

[edit]

1.7. m. learning

다양체학습? 학습,learning
manifold_learning =,manifold_learning =,manifold_learning . manifold_learning
{




...
Naver:manifold learning
Google:manifold learning
YouTube:manifold learning
"manifold learning"
manifold+learning
}

[edit]

2. MKLINK

differential_geometry
symplectic_geometry =,symplectic_geometry =,symplectic_geometry . symplectic_geometry
{
WtEn:symplectic_geometry
WpSp:symplectic_geometry iiiiii
https://en.wikipedia.org/wiki/Symplectic_geometry
}
단위원판,unit_disk =단위원판,unit_disk =,unit_disk 단위원판 unit_disk
{
WtEn:unit_disk
WpSp:Unit_disk
WpEn:Unit_disk = https://en.wikipedia.org/wiki/Unit_disk

단위,unit 원판,disk
... Namu:단위원판 Libre:단위원판 Ndict:단위원판 Ggl:단위원판 Bing:단위원판
}
열린단위원판,open_unit_disk =열린단위원판,open_unit_disk =,open_unit_disk 열린단위원판 open_unit_disk
{
WtEn:open_unit_disk
WpEn:open_unit_disk


manifold는 shape의 일반화,generalization?
shape에 대한 페이지를 만들어야 하는데... or figure?
모양,shape or 도형,shape or 도형,geometric_shape - 도형이 좀더 기하적인 용어
{
Namu:도형
}


[edit]

3. Bmks

[edit]

3.1. The Bright Side of Mathematics (YouTube)


Manifolds (Playlist)
https://www.youtube.com/playlist?list=PLBh2i93oe2qvRGAtgkTszX7szZDVd6jh1
2023-09-13 현재 Part 20까지 있고 '사용할 수 없는 동영상 5개가 숨겨졌습니다.' + 마지막 Part 20만 dark version 있음, 8일 전. - dark version 만드는 중?
[edit]

3.1.1. 1

[edit]

3.2. the Manifold Atlas Project

[edit]

4. 같은단어

[edit]

4.1. 같은 한국어 단어, 다른 영어 단어:

[edit]

4.2. manifold

[edit]

5. Twins:

----
다양체,manifold Modified on 12:41 pm, December 28, 2023.
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