Contents
- 1. Sub
- 1.1. 벡터공간 vector space
- 1.2. 선형공간 linear space
- 1.3. 부분공간 subspace
- 1.4. 널공간/영공간 중 TBD. nullspace
- 1.5. 표본공간 sample space
- 1.6. 가측공간? measurable space
- 1.7. affine space
- 1.8. metric space
- 1.9. Polish space
- 1.10. Baire space
- 1.11. Hamming space
- 1.12. version space
- 1.13. half-space
- 1.14. homogeneous space
- 1.15. hyperbolic space
- 1.16. T0공간 T0 space = 콜모고로프 공간 Kolmogorov space
- 1.17. T1공간 T1 space
- 1.18. T2공간 T2 space = 하우스도르프 공간 Hausdorff space
- 1.19. Tx 공간 ... tmp (x∈ℕ? - No, see
Separation_axiom and
History_of_the_separation_axioms보면 분수도 보인다. (간단히는 오른쪽 표))
- 1.20. 위상공간 topological space
- 1.21. 바나흐 공간 Banach space
- 1.22. 유클리드 공간 Euclidean space
- 1.23. configuration space (물리)
- 1.24. 곱공간 product space
- 1.25. ADDHERE(무슨공간)
- 1.26. ADDHERE(무슨공간)
- 1.27. ADDHERE(무슨공간)
- 1.28. ADDHERE(무슨공간)
- 1.29. ADDHERE(무슨공간)
- 1.30. ADDHERE(무슨공간)
- 2. 공간/space 관련 주제/Topics
- 3. 수학의 공간이 아닌 공간
- 4. ...
1.7. affine space ¶
affine space
아핀공간 ?
아핀공간 ?
MKL incidence_geometry =,incidence_geometry =,incidence_geometry . incidence_geometry
{
incidence geometry
incidence geometry
{
incidence geometry
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
https://commons.wikimedia.org/wiki/Category:Incidence_geometry
incidence geometry
incidence geometry
"Incidence geometry is one of the most abstract geometric_structure in which only the irreflexive_relation {
irreflexive_relation } of incidence is considered."
"incidence geometry"![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
Rel
incidence =,incidence =,incidence . incidence
affine_plane
affine_plane
Affine_plane_(incidence_geometry)
= https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)
= https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)
}
incidence =,incidence =,incidence . incidence
{
incidence
incidence = https://en.wiktionary.org/wiki/incidence#Noun
syn. occurrence? <- n., occur v. ?
}
incidence_system =,incidence_system =,incidence_system . incidence_system![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
syn. occurrence? <- n., occur v. ?
}
{
incidence system
MKL
incidence_structure =,incidence_structure . incidence_structure
Twins:
https://encyclopediaofmath.org/wiki/Incidence_system
"incidence system"
incidence system
incidence system
Up: incidence 시스템,system
} //
MKL 아핀평면,affine_plane { =아핀평면,affine_plane =,affine_plane . incidence system
MKL
incidence_structure =,incidence_structure . incidence_structure
{
incidence structure
incidence_structure = https://en.wiktionary.org/wiki/incidence_structure
MKL: incidence_system
Up: incidence structure
"incidence structure"
incidence structure
incidence structure
} // incidence structure
incidence_matrix =,incidence_matrix . incidence_matrixincidence structure
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
MKL: incidence_system
Up: incidence structure
"incidence structure"
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
} // incidence structure
{
incidence matrix
incidence_matrix = https://en.wiktionary.org/wiki/incidence_matrix
incidence matrix
incidence matrix
Up: incidence 행렬,matrix
} // incidence matrix
https://en.wiktionary.org/wiki/incidence_system x 2023-11-06incidence matrix
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
"(graph theory) A matrix showing the relationship between two classes of objects." (2023-11-06)
"incidence matrix"![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
Up: incidence 행렬,matrix
} // incidence matrix
Twins:
https://encyclopediaofmath.org/wiki/Incidence_system
"incidence system"
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
Up: incidence 시스템,system
} //
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
= https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)
= https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)
}
Sub:
Moulton_plane =,Moulton_plane =,Moulton_plane . Moulton_plane {
Moulton_plane https://en.wikipedia.org/wiki/Moulton_plane
Moulton plane
Moulton plane
Moulton plane
"Moulton plane"
}
Moulton_plane =,Moulton_plane =,Moulton_plane . Moulton_plane {
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
Moulton plane
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"Moulton plane"
}
1.8.1. (+ complete metric space) ¶
metric space
측도공간 or 계량공간 or 거리공간 ... metric_space
// ....
측도공간
측도공간
측도공간 (?? 측도,measure ... measure_space ?
measure_space
measure.space )
// ....
계량공간
계량공간
계량공간이라 번역할 수는 없는지? (? metric 이 n. 이라면 이렇게 할 수 있지만 adj. 라면 의미 없는데 ...
metric
metric
metric )
cf. 계량,metric =계량,metric =,metric 계량 metric
{
// ....
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
// ....
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
cf. 계량,metric =계량,metric =,metric 계량 metric
{
Twins:
kms는 거리공간이라 함.
거리공간,metric_space =거리공간,metric_space =,metric_space . metric_space 거리공간
계량공간,metric_space ?
계량공간
계량공간
계량공간
{
거리공간
metric space
계량공간,metric_space ?
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
{
거리공간
metric space
complete_metric_space {
완비거리공간 ?
complete metric space
complete_metric_space
https://proofwiki.org/wiki/Definition:Complete_Metric_Space
"complete metric space"
}
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
complete metric space
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://proofwiki.org/wiki/Definition:Complete_Metric_Space
"complete metric space"
}
1.9.1. (+ effective Polish space) ¶
폴란드_공간,Polish_space =,Polish_space . Polish_space {
Polish_space https://en.wikipedia.org/wiki/Polish_space
Polish space "Polish space"}
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
effective_Polish_space { effective Polish space https://en.wikipedia.org/wiki/Effective_Polish_space
effective_Polish_space x 2023-08-29
effective Polish space "effective Polish space"}
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
1.11. Hamming space ¶
해밍_공간,Hamming_space =,Hamming_space =,Hamming_space . Hamming_space
{
해밍_코드,Hamming_code { curr.
해밍_코드,Hamming_code https://en.wikipedia.org/wiki/Hamming_code }
문자열,string > binary_string
{
해밍_코드,Hamming_code { curr.
![VG: VG:](/wiki/imgs/interwiki/vg-16.png)
문자열,string > binary_string
1.12.1. (+ version space learning) ¶
version_space_learning =,version_space_learning . version_space_learning
버전공간학습 ?
버전공간학습 ?
ML(특히 이진분류,binary_classification)에 대한 logical(linked to:
Symbolic_artificial_intelligence / rel. logic_programming ) approach.
https://en.wikipedia.org/wiki/Version_space_learning
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
https://en.wikipedia.org/wiki/Version_space_learning
(Redirected from Version space)
버전,version 학습,learning1.13. half-space ¶
1.15. hyperbolic space ¶
hyperbolic_space =,hyperbolic_space =,hyperbolic_space . hyperbolic_space
![WpKo: WpKo:](/wiki/imgs/interwiki/wpko-16.png)
"쌍곡 기하학(쌍곡기하학 hyperbolic_geometry ?)에서 쌍곡공간(雙曲空間, 영어: hyperbolic space)은 균일한 음의 곡률,curvature을 갖는 동차공간이다."
(쌍곡평면에서 넘어옴)
(쌍곡평면에서 넘어옴)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
MKL 쌍곡기하 hyperbolic_geometry =,hyperbolic_geometry =,hyperbolic_geometry . hyperbolic_geometry {
hyperbolic_geometry https://mathworld.wolfram.com/HyperbolicGeometry.html https://ko.wikipedia.org/wiki/쌍곡기하학 https://simple.wikipedia.org/wiki/Hyperbolic_geometry https://en.wikipedia.org/wiki/Hyperbolic_geometry (Redirected from
Hyperbolic_plane) Up: 비유클리드_기하 의 일종. non-Euclidean_geometry }
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
(MISC, DEL) 2023-08-29 현재 redirections: Wikipedia English: 쌍곡평면 redir to 쌍곡기하 / Wikipeida Korean: 쌍곡평면 redir to 쌍곡공간
1.16. T0공간 T0 space = 콜모고로프 공간 Kolmogorov space ¶
pagename?
"T0 공간"
T0공간 T_0공간 ....
T0 공간"T0 공간"
콜모고로프 공간
콜모고로프_공간
Kolmogorov space
Kolmogorov_space
콜모고로프_공간
Kolmogorov space
Kolmogorov_space
콜모고로프_공간,Kolmogorov_space =,Kolmogorov_space . Kolmogorov_space
1.18. T2공간 T2 space = 하우스도르프 공간 Hausdorff space ¶
하우스도르프 공간
(수백:)
서로 다른 두 점,point을 열린집합,open_set으로 분리
separation?
distinctness ?할 수 있는 위상공간,topological_space
AKA T2공간
거리공간,metric_space(
metric_space측도공간?
측도공간
metric_space )은 하우스도르프 공간임.
서로 다른 두 점,point을 열린집합,open_set으로 분리
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
AKA T2공간
거리공간,metric_space(
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
...
하우스도르프 공간
하우스도르프 공간
하우스도르프 공간
"하우스도르프 공간"
Hausdorff space x
Hausdorff space
Hausdorff space
Hausdorff space
"Hausdorff space"
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"하우스도르프 공간"
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"Hausdorff space"
1.19. Tx 공간 ... tmp (x∈ℕ? - No, see
Separation_axiom and
History_of_the_separation_axioms보면 분수도 보인다. (간단히는 오른쪽 표)) ¶
1.21. 바나흐 공간 Banach space ¶
바나흐 공간
Banach space
Banach space
바나흐_공간,Banach_space =바나흐_공간,Banach_space =,Banach_space . Banach_space
1.23. configuration space (물리) ¶
configuration space
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
2.1. space partitioning .. 공간분할 ?? ¶
partitioning space:
space_partitioning =,space_partitioning =,space_partitioning . space_partitioning { 공간분할 ? https://en.wikipedia.org/wiki/Space_partitioning }
공간분할
공간분할
공간분할
space_partitioning =,space_partitioning =,space_partitioning . space_partitioning { 공간분할 ? https://en.wikipedia.org/wiki/Space_partitioning }
binary_space_partitioning =,binary_space_partitioning . binary_space_partitioning (BSP) |=,BSP BSP
{
Euclidean_space 를 hyperplane 상의 볼록집합,convex_set으로 partitioning(분할,partition하기)하는 기법, data_structure 트리,tree구조인 BSP_tree ... (wk)
REL
이진탐색,binary_search
이진트리,binary_tree
binary_space_partition =,binary_space_partition . binary_space_partition |=,BSP BSP
{
3D Rendering with Binary Space Partitions - YouTube
https://www.youtube.com/watch?v=yTRzfKh4Tg0
차례로
painter's algorithm - too much overdrawing
raycasting - 모든 x좌표를 훑어야 함
BSP - no overdrawing
을 알아봄.
}
https://ko.wikipedia.org/wiki/이진_공간_분할법
https://en.wikipedia.org/wiki/Binary_space_partitioning
}
Euclidean_space 를 hyperplane 상의 볼록집합,convex_set으로 partitioning(분할,partition하기)하는 기법, data_structure 트리,tree구조인 BSP_tree ... (wk)
REL
이진탐색,binary_search
이진트리,binary_tree
binary_space_partition =,binary_space_partition . binary_space_partition |=,BSP BSP
{
3D Rendering with Binary Space Partitions - YouTube
https://www.youtube.com/watch?v=yTRzfKh4Tg0
차례로
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
raycasting - 모든 x좌표를 훑어야 함
BSP - no overdrawing
을 알아봄.
}
https://ko.wikipedia.org/wiki/이진_공간_분할법
https://en.wikipedia.org/wiki/Binary_space_partitioning
}
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
공간분할
3. 수학의 공간이 아닌 공간 ¶
conceptual_space =,conceptual_space . conceptual_space
Conceptual_space
rel 개념,concept?
conceptual_space
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
rel 개념,concept?
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
문자,character / 문서,document / ....에서 space는
//TODO TOMERGE : 화이트스페이스,whitespace
whitespace character -> 공백,whitespace or 공백문자,whitespace_character? =,whitespace =,whitespace_character
//TODO TOMERGE : 화이트스페이스,whitespace
whitespace character -> 공백,whitespace or 공백문자,whitespace_character? =,whitespace =,whitespace_character
{
whitespace character
유니코드 Whitespace(공백) 문자 모음 | GeekNews
https://news.hada.io/topic?id=2604
MKL:
tab_character
backspace_character
띄어쓰기
Sub:
줄바꿈없는공백(문자) NBSP =,nbsp .
https://namu.wiki/w/공백
https://ko.wikipedia.org/wiki/공백_문자
Up:
문자,character
특수문자,special_character?
} // whitespace character ....
whitespace character
whitespace
whitespace
whitespace character
유니코드 Whitespace(공백) 문자 모음 | GeekNews
https://news.hada.io/topic?id=2604
MKL:
tab_character
backspace_character
띄어쓰기
https://namu.wiki/w/띄어쓰기
에선 word spacing ...
word spacing
띄어쓰기 ....근데 일반적인 spacing 얘기보다는, 주로 한국어 문법/맞춤법 얘기. (opp. 붙여쓰기 -
붙여쓰기 )
보통 문자체계/기록/script/writing and printing/......에서 단어,word의 구분을 위한?
indentation에선 word spacing ...
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Namu: Namu:](/wiki/imgs/interwiki/namu-16.png)
보통 문자체계/기록/script/writing and printing/......에서 단어,word의 구분을 위한?
Sub:
줄바꿈없는공백(문자) NBSP =,nbsp .
rel. newline
https://namu.wiki/w/NBSP
soft_hyphen SHYhttps://namu.wiki/w/NBSP
아래아한글 2.x에서 '묶음빈칸'이라는 기능이 있었다고 ... 번역어 후보?
"웹 문서에서는 CSS로 "word-break: keep-all;" 속성을 주면, 영어뿐만 아니라 한글에서도 NBSP를 적용할 수 있다."
"웹 문서에서는 CSS로 "word-break: keep-all;" 속성을 주면, 영어뿐만 아니라 한글에서도 NBSP를 적용할 수 있다."
https://ko.wikipedia.org/wiki/공백_문자
Up:
문자,character
특수문자,special_character?
} // whitespace character ....
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)