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Encyclopedia of Compactness の変更点


 *注意 [#e7a65568]
 このページの説明です。
 **このページの収集対象 [#p9f31ae3]
 -ここは「ナントカコンパクト」という用語の定義を集めたページです。
 --基本的に''位相空間またはその部分集合''の性質として数学の文献に載ったナントカコンパクトという用語を集めています。
 --例えばfunctional analysisにおけるcompact operatorや、order theoryにおけるcompact elementなどは対象外です。そういったものは[[Other Compactness]]へ。
 -あくまでcompactがついているものだけ載せてください。
 --Lindeloefなどは、compactと関連の強い概念ですが「compact」がつかないので対象外です(ただし、「Lindeloef compact」は有りです)。
 --compactumは対象に入ります。
 -数学の公的なジャーナル、書籍などに記載されたものに限ります。
 --プレプリントやWikipedia等のウェブサイトの記述はソースとして認めません。
 -bitopologyやfuzzy topology, supratopology, L-cotopology等の用語については[[Bitopology and Fuzzy Topology etc.]]にお願いします。
 --対象についての詳細は[[Bitopology and Fuzzy Topology etc.]]の注意を見てください。
 -bitopologyやfuzzy topologyにも該当しないcompactについては、[[Other Compactness]]にお願いします。
 --compactoidは[[Other Compactness]]にお願いします。
 **編集のルール [#e374b029]
 -出典をかならず明記してください。なるべく初出のものが望ましいです。
 --出典は、詳しい内容を知りたい人のための情報というだけでなく、「その用語が実際に数学の文献に載った証拠」という意味もあります。これは「ナントカコンパクトってどれくらいあるのか調べてみよう」というこのページの当初の動機から来ています。なので「出典はなくても分かるだろう」と省略しないでください。
 -書式は[[テンプレ]]の項を参考にしてください。
 -同一の用語が同値でない二つの定義を持つ場合、以下のいずれかで対処してください。
 --一つのページに二つの定義を併記する。
 --適当にページ名を分け、それぞれの用語の説明を記述した二つのページと曖昧さ回避のページを作り、曖昧さ回避のページのリンクを索引に貼る。
 -用語を区別する際、大文字・小文字の違い、フォントの違い、ハイフン・空白の有無は無視します。
 --例えばsemi compactとsemi-compact、semicompactは同一の用語とみなします。
 --CO-compactとco-compactは同一の用語とみなします。
 --\mathbb{N}-compactとN-compactは同一の用語とみなします。
 -実際の名称とページ名が異なる場合があります。その際実際の名称はページの先頭に記してあります。
 --たとえば[[[a,b]-chain compact>(a,b)-chain compact]]は"["をページ名に使うことが出来ないため"(a,b)-chain compact"というページ名で登録しています。
 -索引の並びはハイフン・空白を無視した辞書式順序でお願いします。
 -気になることがあったら[[編集ノート]]に書いてください。
 **規約 [#g2e3e283]
 特に記述のない限り、以下の規約が優先されます。
 COLOR(red){暫定案です。ご意見ご提案は[[編集ノート]]にお願いします。}
 -公理系はZFCを採用。
 -Tychonoffはcompletely regularと同義。
 -completely normalとhereditarily normalは同義。
 -regular, completely regular, normal, completely normal, perfectly normalにはT_1を要求する。
 -T_3, T_{3 1/2}, T_4, T_5, T_6にはT_1を要求しない。
 -compactにはT_2であることを要求しない。
 -k-spaceにはT_2であることを要求しない。
 -paracompactにはT_2であることを要求しない。
 -neighberhoodはopenとは限らない。
 -locally convex spaceはT_2であることを要求する。
 -topological manifoldはsecond countableであることを要求しない。
 -βXはStone-Cech compactificationを、υXはHewitt-Nachbin realcompactificationを表わす。
 *索引 [#i2362eb9]
 [[数字>#zdd5ddf6]] [[A>#l04c50e0]] [[B>#x5a96df4]] [[C>#a3478ac7]] [[D>#b94c798f]] [[E>#p1b79239]] [[F>#r426fb67]] [[G>#f5c6f7ee]] [[H>#q7514866]] [[I>#g01b4d57]] [[J>]] [[K>#we5e8c23]] [[L>#ra2a0531]] [[M>#f5678783]] [[N>#d6911f69]] [[O>#r947dbbb]] [[P>#pc6e905b]] [[Q>#xf7d7bea]] [[R>#nabfdfcf]] [[S>#pa539aa9]] [[T>#h9c55279]] [[U>#z4da3e44]] [[V>]] [[W>#l4ab8c6f]] [[X>]] [[Y>]] [[Z>#i427468c]] [[ギリシャ文字>#g25479ac]] [[記号>#t717c7ba]]
 
 ** [#x7b67888]
 -[[compact]]
 
 **数字 [#zdd5ddf6]
 -[[1 1/2-starcompact]]
 -[[1-countably paracompact]]
 -[[1-metacompact]]
 -[[1-paracompact]]
 -[[1-starcompact]] 
 -[[1-subparacompact]]
 -[[2-countably paracompact]]
 -[[2-metacompact]]
 -[[2-paracompact]]
 -[[2-subparacompact]]
 -[[3-paracompact]]
 **A [#l04c50e0]
 -[[AB-compactum]]
 -[[absolutely countably compact]]
 -[[absolutely paracompact]]
 -[[adherent compact]]
 -[[Alexandroff-Urysohn-compact]]
 -[[almost co-compact]]
 -[[almost-compact]]
 -[[almost countably base-compact]]
 -[[almost countably paracompact]]
 -[[almost countably subcompact]]
 -[[almost locally compact]]
 -[[almost m-paracompact]]
 -[[almost paracompact]]
 -[[almost precompact]]
 -[[almost preorthocompact]]
 -[[almost realcompact]]
 -[[almost rim-compact]]
 -[[almost $\mathbb{R}$-paracompact]]
 -[[almost strongly paracompact]]
 -[[almost weakly paracompact]]
 -[[almost π-compact]]
 -[[almost σ-compact]]
 -[[almost* realcompact]]
 -[[almost (m,n)-paracompact]]
 -[[angelic compact]]
 -[[anti-compact]]
 -[[anti-countably compact]]
 -[[anti-paracompact]]
 -[[anti-pseudocompact]]
 -[[anti-semi compact]]
 -[[anti-sequentially compact]]
 -[[anti-σ-compact]]
 -[[a-paracompact]]
 -[[a-realcompact]]
 -[[Aull-paracompact]]
 **B [#x5a96df4]
 -[[base-base hypocompact]]
 -[[base-base metacompact]]
 -[[base-base paracompact]]
 -[[base-base ultraparacompact]]
 -[[base-compact]]
 -[[base-cover hypocompact]]
 -[[base-cover metacompact]]
 -[[base-cover paracompact]]
 -[[base-family hypocompact]]
 -[[base-family metacompact]]
 -[[base-family paracompact]]
 -[[base paracompact]]
 -[[basically paracompact]]
 -[[b-compact]]
 -[[B-completely paracompact]]
 -[[bicompact]] COLOR(RED){(Citation Needed)}
 -[[Bolzano-Weierstrass compact]]
 -[[boundedly metacompact]]
 -[[boundedly paracompact]]
 -[[Bourbaki-compact]]
 -[[B-paracompact]]
 -[[B-strongly paracompact]]
 -[[B-subcompact]]
 -[[B-superparacompact]]
 **C [#a3478ac7]
 -[[CB-compact]]
 -[[CCL-compact]]
 -[[C-compact]]
 -[[chain compact]]
 -[[c-isocompact]]
 -[[cl-isocompact]]
 -[[closure C-compact]]
 -[[closure compact]]
 -[[Clp-compact]]
 -[[co-compact(Disambiguation)]]
 -[[coparacompact]]
 -[[CO-superparacompact]]
 -[[Comfort-compact]]
 -[[compact-boundary compact]]
 -[[compactly functionally compact]]
 -[[completely paracompact]]
 -[[computably based locally compact]]
 -[[conditionally compact]]
 -[[core compact]]
 -[[Corson compact]]
 -[[countably 1-paracompact]]
 -[[countably 2-paracompact]]
 -[[countably 3-paracompact]]
 -[[countably absolutely countably compact]]
 -[[countably almost-compact]]
 -[[countably almost preorthocompact]]
 -[[countably Aull-pracompact]]
 -[[countably B-subcompact]]
 -[[countably base-compact]]
 -[[countably CB-compact]]
 -[[countably Clp-compact]]
 -[[countably compact]]
 -[[countably FB-compact]]
 -[[countably I-compact (Disambiguation)]]
 -[[countably metacompact]]
 -[[countably paracompact]]
 -[[countably P-compact]]
 -[[countably P-completely paracompact]]
 -[[countably P-paracompact]]
 -[[countably preorthocompact]]
 -[[countably P-strongly paracompact]]
 -[[countably P-superparacompact]]
 -[[countably rc-compact]]
 -[[countably starcompact]]
 -[[countably strongly paracompact]]
 -[[countably subcompact]]
 -[[countably subparacompact]]
 -[[countably γ-closed-compact]]
 -[[countably γ-compact]]
 -[[countably ν-compact]]
 -[[c-realcompact]]
 -[[cs-starcompact]]
 -[[C_α-compact]]
 **D [#b94c798f]
 -[[d-compact]]
 -[[densely countably compact]]
 -[[D-feebly compact]]
 -[[discretely orthocompact]]
 -[[D-paracompact]]
 -[[D-pseudocompact]]
 -[[Dugundji compact]]
 -[[dyadic compact]]
 -[[D_δ-compact]]
 -[[d*-compact]]
 **E [#p1b79239]
 -[[Eberlein compact]]
 -[[e-compact (Disambiguation)]]
 -[[e-countably compact]]
 -[[e-paracompact]]
 **F [#r426fb67]
 -[[FB-compact]]
 -[[F-compact]]
 -[[feebly compact]]
 -[[finally compact]]
 -[[finally α-compact]]
 -[[finely paracompact]]
 -[[finite-boundary compact]]
 -[[finitely compact]]
 -[[finitely functionally compact]]
 -[[F-paracompact]]
 -[[Frechet-compact]]
 -[[fully pseudocompact]]
 -[[functionally compact]]
 **G [#f5c6f7ee]
 -[[GO-compact]]
 -[[GPO-compact]]
 -[[GSO-compact]]
 -[[Gul'ko compact]]
 -[[G_δ-relatively realcompact]]
 **H [#q7514866]
 -[[Heine-Borel-compact]]
 -[[hemicompact]]
 -[[Hilbert compact]]
 -[[hypercompact]]
 -[[hyperisocompact]]
 -[[hypocompact]]
 **I [#g01b4d57]
 -[[I-compact (Disambiguation)]]
 -[[initially κ-compact]]
 -[[I-paracompact (paracompact modulo I)]]
 -[[isocompact]]
 -[[isoparacompact]]
 **K [#we5e8c23]
 -[[K-starcompact]]
 **L [#ra2a0531]
 -[[left locally compact]]
 -[[lightly compact]]
 -[[lightly paracompact]]
 -[[limit point compact]]
 -[[line-compact]]
 -[[Lindeloef compact]] COLOR(red){(Citation Needed)}
 -[[locally almost compact]]
 -[[locally almost paracompact]]
 -[[locally C-compact]]
 -[[locally compact]]
 -[[locally hypercompact]]
 -[[locally nearly-compact]]
 -[[locally peripherally compact]]
 -[[locally strongly pseudocompact]]
 -[[locally supercompact]]
 -[[locally truly weakly pseudocompact]]
 -[[locally weakly pseudocompact]]
 -[[locally κ-hypercompact]]
 -[[locally ν-compact]]
 **M [#f5678783]
 -[[m-metacompact]]
 -[[m-paracompact]]
 -[[m-pseudocompact]]
 -[[m-quasicompact]]
 -[[mean compact]]
 -[[measure-compact]]
 -[[mesocompact]]
 -[[metacompact]]
 -[[microcompact]]
 -[[microquasi-compact]]
 -[[mildly compact]]
 -[[mildly countably compact]]
 -[[mildly paracompact]]
 -[[monotonically compact]]
 -[[monotonically countably compact]]
 -[[monotonically countably metacompact]]
 -[[monotonically metacompact]]
 -[[monotonically orthocompact]]
 -[[monotonically paracompact]]
 **N [#d6911f69]
 -[[n-boundedly metacompact]]
 -[[n-boundedly paracompact]]
 -[[N-compact (Disambiguation)]]
 -[[nearly compact]]
 -[[nearly countably compact]]
 -[[nearly locally compact]]
 -[[nearly metacompact]]
 -[[nearly paracompact]]
 -[[nearly pseudocompact]]
 -[[nearly realcompact]]
 -[[nearly strongly paracompact]]
 -[[nearly weakly paracompact]]
 -[[net-compact]]
 -[[nomally supercompact]]
 -[[nowhere compact]]
 -[[nowhere locally compact]]
 -[[NS compact]]
 -[[n-starcompact]]
 **O [#r947dbbb]
 -[[order totally paracompact]]
 -[[orthocompact]]
 **P [#pc6e905b]
 -[[P_1-paracompact]]
 -[[P_2-paracompact]]
 -[[P_3-paracompact]]
 -[[paracompact]]
 -[[pc-compact]]
 -[[p-compact]]
 -[[P-completely paracompact]]
 -[[perfectly compact]]
 -[[peripherally bicompact]]
 -[[peripherally compact]]
 -[[peripherally C-compact]]
 -[[point-finitely paracompact]]
 -[[point-star compact]]
 -[[point-star metacompact]]
 -[[point-star orthocompact]]
 -[[point-star paracompact]]
 -[[point-star preorthocompact]]
 -[[pointwise countably paracompact]]
 -[[pointwise m-paracompact]]
 -[[pointwise paracompact]]
 -[[pointwise star-orthocompact]]
 -[[potentially compact]]
 -[[potentially pseudocompact]]
 -[[P-paracompact]]
 -[[p-pseudocompact]]
 -[[p-realcompact]]
 -[[precompact]]
 -[[preorthocompact]]
 -[[preparacompact]]
 -[[pseudocompact]]
 -[[pseudoparacompact]]
 -[[pseudo-(α,β)-compact]]
 -[[P-strongly paracompact]]
 -[[P-superparacompact]]
 **Q [#xf7d7bea]
 -[[quasicompact]]
 -[[quasi locally compact]]
 -[[quasi-paracompact]]
 **R [#nabfdfcf]
 -[[Radon-Nikodym compact]]
 -[[rc-compact]]
 -[[R-completely paracompact]]
 -[[realcompact]]
 -[[regularly co-compact]]
 -[[relatively compact>relatively compact (Disambiguation)]]
 -[[relatively countably compact]]
 -[[relatively pseudocompact]]
 -[[relatively realcompact]]
 -[[relatively rightly compact]]
 -[[relatively sequentially compact]]
 -[[retrocompact]]
 -[[right locally compact]]
 -[[rim-compact]]
 -[[RN compact]]
 -[[Rosenthal-Banach compact]]
 -[[Rosenthal compact]]
 -[[R-paracompact (Disambiguation)]]
 -[[RS-compact]]
 -[[R-strongly paracompact]]
 -[[R-superparacompact]]
 **S [#pa539aa9]
 -[[SC-compact]]
 -[[s-compact]]
 -[[self-compact]]
 -[[semibicompact]]
 -[[semicompact]]
 -[[semi-countably compact]]
 -[[semi-generalized compact]]
 -[[semi-metacompact]]
 -[[semi-θ-compact]]
 -[[sequentially compact]]
 -[[sequentially mesocompact]]
 -[[sequentially p-compact]]
 -[[sequentially s-compact]]
 -[[sequentially sp-compact]]
 -[[sequentially α-compact]]
 -[[sg-compact]]
 -[[SGO-compact]]
 -[[slightly compact]]
 -[[S-metacompact]]
 -[[s-paracompact (Disambiguation)]]
 -[[stably compact]]
 -[[stably locally compact]]
 -[[starcompact]]
 -[[starparacompact]]
 -[[strictly Aull-paracompact]]
 -[[strictly paracompact]]
 -[[strong cover compact]]
 -[[strongly C-compact]]
 -[[strongly compact]]
 -[[strongly countably paracompact]]
 -[[strongly isocompact]]
 -[[strongly locally compact]]
 -[[strongly locally pseudocompact]]
 -[[strongly measure-compact]]
 -[[strongly m-paracompact]]
 -[[strongly n-starcompact]]
 -[[strongly paracompact]]
 -[[strongly peripherally bicompact]]
 -[[strongly pseudocompact]]
 -[[strongly relatively pseudocompact]]
 -[[strongly τ-pseudocompact]]
 -[[subcompact]]
 -[[submesocompact]]
 -[[submetacompact]]
 -[[suborthocompact]]
 -[[subparacompact]]
 -[[supercompact]]
 -[[super countably paracompact]]
 -[[supermetacompact]]
 -[[superparacompact]]
 -[[supersubmetacompact]]
 -[[super-Valdivia compact]]
 **T [#h9c55279]
 -[[Talagrand compact]]
 -[[thick compact]]
 -[[totally countably compact]]
 -[[totally metacompact]]
 -[[totally paracompact]]
 -[[truly weakly pseudocompact]]
 **U [#z4da3e44]
 -[[ultracompact]]
 -[[ultraparacompact]]
 -[[ultrapseudocompact]]
 -[[uniform Eberlein compact]]
 -[[uniformly compact]]
 -[[uniformly locally compact]]
 -[[uniformly paracompact]]
 -[[uniformly strongly paracompact]]
 -[[uniformly superparacompact]]
 -[[uniformly σ-compact]]
 **V [#ldf90a33]
 -[[Valdivia compact]]
 **W [#l4ab8c6f]
 -[[wa-realcompact]]
 -[[weak cover compact]]
 -[[weakly compact]]
 -[[weakly countably compact]]
 -[[weakly Frechet compact>weakly Frechet compact (Disambiguation)]]
 -[[weakly metacompact]]
 -[[weakly orthocompact]]
 -[[weakly paracompact]]
 -[[weakly pre-compact]]
 -[[weakly pseudocompact]]
 -[[weakly realcompact]]
 -[[weakly suborthocompact]]
 -[[weakly submetacompact]]
 -[[weakly superparacompact]]
 -[[weakly κ-suborthocompact]]
 -[[weakly κ-submetacompact]]
 -[[weakly (m,n)-paracompact]]
 -[[Weierstrass-compact]]
 **Z [#i427468c]
 -[[Z-pseudocompact]]
 
 **ギリシャ文字 [#g25479ac]
 -[[α-almost paracompact]]
 -[[α-almost $\mathbb{R}$-paracompact]]
 -[[α-compact]]
 -[[α-countably paracompact]]
 -[[α-nearly compact]]
 -[[α-nearly paracompact]]
 -[[α-paracompact]]
 -[[α-pseudocompact]]
 -[[α-realcompact]]
 -[[β-compact]]
 -[[γ-closed-compact]]
 -[[γ-compact]]
 -[[γ-paracompact]]
 -[[γ-strongly paracompact]]
 -[[γ-weakly paracompact]]
 -[[δ-compact]]
 -[[η-compact]]
 -[[θ-compact]]
 -[[κ-hypercompact]]
 -[[κ-metacompact]]
 -[[κ-orthocompact]]
 -[[κ-suborthocompact]]
 -[[λ-compact]]
 -[[μ-compact]]
 -[[ν-compact>ν-compact (Disambiguation)]]
 -[[π-bicompact]]
 -[[π-compact]]
 -[[σ-compact]]
 -[[σ-C_α-compact]]
 -[[σ-line-compact]]
 -[[σ-locally compact]]
 -[[σ-metacompact]]
 -[[σ-orthocompact]]
 -[[σ-paracompact]]
 -[[σ-pseudocompact]]
 -[[σ-totally paracompact]]
 -[[σ-α-pseudocompact]]
 -[[σ-ν-compact]]
 -[[τ-completely paracompact]]
 -[[τ-P-completely paracompact]]
 -[[τ-P-paracompact]]
 -[[τ-pseudocompact]]
 -[[τ-P-strongly paracompact]]
 -[[τ-P-superparacompact]]
 -[[τ-strongly paracompact]]
 -[[ψ-compact]]
 -[[ω-starcompact]]
 **記号 [#t717c7ba]
 -[[[a,b]-chain compact>(a,b)-chain compact]]
 -[[[a,b]-compact>(a,b)-compact]]
 -[[[a,b]^r-chain compact>(a,b)^r-chain compact]]
 -[[[a,b]^r-compact>(a,b)^r-compact]]
 -[[[a,∞]-compact>(a,∞)-compact]]
 -[[(m,n)-paracompact]]
 -[[(α,β)-metacompact]]
 -[[(Λ,sθ)-compact]]
 -[[\aleph_1-compact>Aleph_1-compact]]
 -[[\aleph-preparacompact]]
 *用語の補足 [#q1b05dfd]
 -[[almost complete]]
 -[[binary subbase]]
 -[[b-open]]
 -[[ccip]] (closed countable intersection property)
 -[[chain net]]
 -[[character]]
 -[[cip]] (countable intersection property)
 -[[closure-preserving]]
 -[[compact-finite]]
 -[[convergent sequence finite]]
 -[[co-open]]
 -[[countably K-determined]]
 -[[cozero set]]
 -[[developable space]]
 -[[Dunford-Pettis operator]]
 -[[finite component cover]]
 -[[fip]] (finite intersection property)
 -[[g-open]] (generalized open)
 -[[gp-open]] (generalized preopen)
 -[[gs-open]] (generalized semiopen)
 -[[H-closed]]
 -[[ideal (family of subsets)]]
 -[[interior-preserving]]
 -[[K-analytic]]
 -[[Lindeloef]]
 -[[line-closed]]
 -[[locally finite]]
 -[[locally-n]]
 -[[maximal (cover)>maximal]]
 -[[network]]
 -[[network weight]]
 -[[normal lower semicontinuous (function)>normal lower semicontinuous]]
 -[[normal subbase]]
 -[[open filter adherence]]
 -[[order locally finite]]
 -[[order (point-finiteness)]]
 -[[partial refinement]]
 -[[p-convergent]]
 -[[perfect (mapping)>perfect]]
 -[[p-locally finite]]
 -[[point-finite]]
 -[[preinterior]]
 -[[preopen]]
 -[[quasi H-closed]]
 -[[regular filter base]]
 -[[regular G_δ set]]
 -[[regular open]]
 -[[S-closed]]
 -[[s-convergent]]
 -[[semiclosed]]
 -[[semiinterior]]
 -[[semiopen]]
 -[[semipreopen]]
 -[[semi-regular]]
 -[[semi-θ-closed]]
 -[[sg-open]] (semi-generalized open)
 -[[shrinking]]
 -[[sober space]]
 -[[sp-convergent]]
 -[[stable family]]
 -[[star-countable]]
 -[[star-finite]]
 -[[strongly open F_σ set]]
 -[[ultranormal]]
 -[[weakly uniform cover]]
 -[[weight (of topological space)]]
 -[[zero set]]
 -[[z-filter]]
 -[[α-convergent]]
 -[[α-open]]
 -[[β-open]]
 -[[γ-open]]
 -[[δ-close]]
 -[[δ-cluster point]]
 -[[δ-open]]
 -[[θ-open]]
 -[[ν-open]]
 -[[π-base]]
 -[[σ-discrete]]
 -[[σ-locally finite]]
 -[[Σ-subset]]
 -[[τ-additive]]
 -[[(Λ,sθ)-closed]]
 
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