1. Sub ¶

1.1. 벡터공간 vector space ¶

1.2. 선형공간 linear space ¶

1.3. 부분공간 subspace ¶

1.4. 널공간/영공간 중 TBD. nullspace ¶

널공간 영공간 null_space nullspace - 영공간,null_space

1.5. 표본공간 sample space ¶

표본공간,sample_space - has moved to 표본공간,sample_space

1.6. 가측공간? measurable space ¶

1.6.1. (+ Borel measurable space) 보렐 가측공간? ¶

1.7. affine space ¶

affine space
아핀공간 ?

아핀공간,affine_space

MKL incidence_geometry =,incidence_geometry =,incidence_geometry . incidence_geometry
{
incidence geometry
incidence geometry

incidence_geometry ? iiiiiiiiiiijjjj
Incidence_geometry

https://commons.wikimedia.org/wiki/Category: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"
incidence geometry
incidence geometry

Rel
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

{
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_matrix

{
incidence matrix
incidence_matrix = https://en.wiktionary.org/wiki/incidence_matrix

"(graph theory) A matrix showing the relationship between two classes of objects." (2023-11-06)

"incidence matrix"
incidence matrix
incidence matrix

Up: incidence 행렬,matrix
} // incidence matrix

https://en.wiktionary.org/wiki/incidence_system x 2023-11-06

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 . 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)
}

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"
}

Affine_space
= https://en.wikipedia.org/wiki/Affine_space

1.8. metric space ¶

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
{

Twins:

천문학백과: 계량 metric

계량

metric

metric

계량

metric

MKL 거리,distance
}

kms는 거리공간이라 함.

거리공간,metric_space =거리공간,metric_space =,metric_space . metric_space 거리공간
계량공간,metric_space ? 계량공간 계량공간 계량공간
{
거리공간
metric space

MKL 계량,metric 거리,distance

https://mathworld.wolfram.com/MetricSpace.html

https://encyclopediaofmath.org/wiki/Metric_space

거리_공간
= https://ko.wikipedia.org/wiki/거리_공간

Metric_space
= https://en.wikipedia.org/wiki/Metric_space

https://www.britannica.com/science/metric-space

거리공간
metric space
metric space
metric space
"metric space"
}

complete_metric_space { 완비거리공간 ?
complete metric space
complete_metric_space
https://proofwiki.org/wiki/Definition:Complete_Metric_Space
"complete metric space"
}

1.9. Polish 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"}

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"}

1.10. Baire space ¶

Baire space
Baire_space

1.10.1. Baire space (set theory) ¶

Baire_space =,Baire_space =,Baire_space . Baire_space (set theory)
{
누구?
발음?

Baire_space_(set_theory)
= https://en.wikipedia.org/wiki/Baire_space_(set_theory)
= https://en.wikipedia.org/wiki/Baire_space_(set_theory)
}

1.10.2. Baire space (topology) ¶

Baire_space =,Baire_space =,Baire_space . Baire_space (topology)
{

베르_공간
= https://ko.wikipedia.org/wiki/베르_공간

Baire_space
= https://en.wikipedia.org/wiki/Baire_space
}

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

Hamming_space

Hamming_space
= https://en.wikipedia.org/wiki/Hamming_space
}

1.12. version space ¶

1.12.1. (+ version space learning) ¶

version_space version_space =,version_space . version_space
version_space
버전공간 ?

version_space_learning =,version_space_learning . version_space_learning
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

(Redirected from Version space)

버전,version 학습,learning

1.13. half-space ¶

half-space =,half-space =,half-space . half-space
{
half space : 반공간

Half-space_(geometry)
= https://en.wikipedia.org/wiki/Half-space_(geometry)
= https://en.wikipedia.org/wiki/Half-space_(geometry)

no wpko(2023-08-24)

반공간

half-space (??)
half-space
half-space
}

chk: hyphen 빼도 되는지? halfspace halfspace halfspace halfspace =,halfspace .

1.14. homogeneous space ¶

동차공간 =동차공간,
homogeneous_space =,homogeneous_space =,homogeneous_space . homogeneous_space

동차공간 (wk)
동차공간, 동질공간 (kms) homogeneous space

homogeneous_space = https://en.wiktionary.org/wiki/homogeneous_space

Homogeneous_space = https://en.wikipedia.org/wiki/Homogeneous_space

동차_공간 = https://ko.wikipedia.org/wiki/동차_공간

...
동차공간
동차공간
동차공간

homogeneous space
homogeneous space
homogeneous space
"homogeneous space"

1.15. hyperbolic space ¶

hyperbolic_space =,hyperbolic_space =,hyperbolic_space . hyperbolic_space

쌍곡공간 = https://ko.wikipedia.org/wiki/쌍곡공간

"쌍곡 기하학(쌍곡기하학 hyperbolic_geometry ?)에서 쌍곡공간(雙曲空間, 영어: hyperbolic space)은 균일한 음의 곡률,curvature을 갖는 동차공간이다."
(쌍곡평면에서 넘어옴)

hyperbolic_space
Hyperbolic_space = https://en.wikipedia.org/wiki/Hyperbolic_space

...
쌍곡공간
쌍곡공간
쌍곡공간
쌍곡공간

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 }

(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?

T0공간 T_0공간 ....

T0 공간
"T0 공간"

콜모고로프 공간
콜모고로프_공간
Kolmogorov space
Kolmogorov_space

콜모고로프_공간,Kolmogorov_space =,Kolmogorov_space . Kolmogorov_space

Kolmogorov_space

Kolmogorov_space = https://simple.wikipedia.org/wiki/Kolmogorov_space x 2023-09-08

Kolmogorov_space

https://proofwiki.org/wiki/Definition:Kolmogorov_Space

T0 공간
T0 공간
T0 공간
"T0 공간"

// Kolmogorov => 콜모고로프. - https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=Kolmogorov

1.17. T₁공간 T₁ space ¶

...
T1 공간
T1 공간
T1 공간
"T1 공간"

1.18. T₂공간 T₂ space = 하우스도르프 공간 Hausdorff space ¶

하우스도르프 공간

(수백:)
서로 다른 두 점,point을 열린집합,open_set으로 분리separation? distinctness ?할 수 있는 위상공간,topological_space
AKA T₂공간
거리공간,metric_space( metric_space측도공간? 측도공간 metric_space )은 하우스도르프 공간임.

수학백과: 하우스도르프 공간

...
하우스도르프 공간
하우스도르프 공간
하우스도르프 공간
"하우스도르프 공간"
Hausdorff space x
Hausdorff space
Hausdorff space
Hausdorff space
"Hausdorff space"

...
T2 공간
T2 공간
T2 공간
"T2 공간"

1.19. Tx 공간 ... tmp (x∈ℕ? - No, see Separation_axiom and History_of_the_separation_axioms보면 분수도 보인다. (간단히는 오른쪽 표)) ¶

1.19.1. T1공간은 T0공간이다. ¶

1.20. 위상공간 topological space ¶

위상공간,topological_space
위상공간,topological_space

위상공간
topological_space
topological space

위상공간
위상공간

topological_space

topological space
"topological space"

1.21. 바나흐 공간 Banach space ¶

바나흐 공간
Banach space

바나흐_공간,Banach_space =바나흐_공간,Banach_space =,Banach_space . Banach_space

Banach_space
바나흐 공간

수학백과: 바나흐 공간

"벡터공간,vector_space에 노름,norm이 정의되어 있으면 노름공간,normed_space이고, 이게 완비성,completeness을 가지면 바나흐 공간이라고 한다."

바나흐 공간
Banach space

1.22. 유클리드 공간 Euclidean space ¶

1.23. configuration space (물리) ¶

configuration space

https://ko.wikipedia.org/wiki/짜임새_공간

configuration_space ?

Configuration_space ? x 2023-11

Configuration_space = https://en.wikipedia.org/wiki/Configuration_space_(mathematics)

물리학,physics에서 상태공간,state_space 및 위상공간,phase_space에 밀접한 개념임

configuration space
configuration space

Up:
configuration =,configuration . configuration

configuration configuration configuration
configuration

1.24. 곱공간 product space ¶

곱공간,product_space =곱공간,product_space =,product_space 곱공간 product_space

product space ?

product_space = https://en.wiktionary.org/wiki/product_space x 2023-11-29

MKL
내적공간,inner_product_space

곱공간 ?

곱공간 ?

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 ¶

2.1. space partitioning .. 공간분할 ?? ¶

partitioning space:
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
}

공간분할
공간분할
공간분할

2.2. and ¶

기저,basis: 공간을 표현하기 위해 최소로 필요한 성분
각 기저들은 직교. 내적하면 0.
그람슈미트직교화

그람-슈미트+직교화
그람-슈미트 직교화
그람-슈미트 직교화

2.3. ADDHERE(공간관련subs) ¶

2.4. ADDHERE(공간관련subs) ¶

2.5. ADDHERE(공간관련subs) ¶

2.6. ADDHERE(공간관련subs) ¶

2.7. ADDHERE(공간관련subs) ¶

2.8. ADDHERE(공간관련subs) ¶

3. 수학의 공간이 아닌 공간 ¶

semantic_space
semantic_space

conceptual_space =,conceptual_space . conceptual_space
Conceptual_space
rel 개념,concept?
conceptual_space

이름공간,namespace - 이름,name, 식별자,identifier

주소공간,address_space - 주소,address

문자,character / 문서,document / ....에서 space는
//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

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?

indentation

Sub:
줄바꿈없는공백(문자) NBSP =,nbsp .

rel. newline
https://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."

soft_hyphen SHY

https://namu.wiki/w/공백

https://ko.wikipedia.org/wiki/공백_문자

Up:
문자,character
특수문자,special_character?

} // whitespace character .... whitespace character whitespace whitespace

4. ... ¶

空間_(数学) = https://ja.wikipedia.org/wiki/空間_(数学)

영단어: 스페이스,space

공간,space

---

Up: 선형대수,linear_algebra