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業務連絡

almost countably base-compactを発見。でもプレプリント。
Definition
A space X is almost countably base-compact if there is a pseudo-base? P for X with the property that if a sequence P_n is a countable centered subcollection of P (i.e., a countable collection of non-empty sets with the finite intersection property), then the closures of P_n has a non-empty intersection.
Reference
http://www.math.wm.edu/~lutzer/drafts/BigBushes.pdf (preprint)

pseudo-base
Definition
A collection P of non-empty open sets of a space X is a pseudo-base (or π-base) for X if for each nonempty open set U, some V in P is contained in U.
Reference
http://www.math.wm.edu/~lutzer/drafts/BigBushes.pdf (preprint)

monotonically ultraparacompact?を発見したが、出典がプレプリントしかないのでまだ掲載できない。
Definition
A topological space X is said to be monotonically ultraparacompact if there is a function m on the set of open covers of X (which is called a monotone ultraparacompactness operator) such that:

  1. if U is an open cover of X, then m(U) is a pairwise disjoint open cover of X which refines U;
  2. if U and V are open covers of X with U refining V, then m(U) refines m(V).

Remark

Reference
http://www.math.wm.edu/~lutzer/drafts/BigBushes.pdf (preprint)

sgc-compact
nearly sgc-compact
S.B. Navalagi, Definition bank in general topology, http://at.yorku.ca/i/d/e/b/75.htm

iso-nearly compact
hereditarily iso-nearly compact
の定義がDefinition Bankに記述されていました
しかしどうやらソースがNavalagiさんの講演だけで論文等には載っていない模様
どうしましょうか

iso-nearly compact
Definition
A topological space is called iso-nearly compact if each of its closed nearly countably compact subsets is nearly compact.

Reference
G.B. Navalagi, The near compactness of nearly countably compact spaces, submitted to Topo2000, 15th Summer Conference, held at Maimi Univesity, Oxford, Miami, USA, on Jul. 26-29, 2000.

hereditarily iso-nearly compact
Definition
A topological space is called hereditarily iso-nearly compact if every subspace is iso-nearly compact space.

Reference
G.B. Navalagi, The near compactness of nearly countably compact spaces, submitted to Topo2000, 15th Summer Conference, held at Maimi Univesity, Oxford, Miami, USA, on Jul. 26-29, 2000.

調査中メモ（未整理）

\mathbb{H}-autocompact
\mathbb{H}-selfcompact
cover-compact
http://math.u-bourgogne.fr/IMB/dolecki/Page/init_IX07.pdf
countercompact
http://www.personal.soton.ac.uk/mgf1v07/docs/2006-01.pdf
proto-compact
http://dml.cz/bitstream/handle/10338.dmlcz/700765/Toposym_03-1971-1_80.pdf
retrocompact
http://www.math.columbia.edu/algebraic_geometry/stacks-git/topology.pdf
sym-compact
http://www.lsv.ens-cachan.fr/Publis/RAPPORTS_LSV/PDF/rr-lsv-2007-34.pdf
discompact (group?)
http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.1423v1.pdf
demicompact (operator?)
http://books.google.co.jp/books?id=HGa99Vi5KEYC&pg=PA180&lpg=PA180&dq=demicompact+topology&source=bl&ots=armgQ-D_yy&sig=WdYbcI0bOrIc3wN5rJ49elYcx98&hl=ja&ei=2KvTTIL6L4GcvgO4wfmZBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBkQ6AEwAA#v=onepage&q=demicompact%20topology&f=false
midcompact (filter?)
infracompact (operator?)

rc-paracompact
T. R. Hamlett, D. Jankovi´c, and Ch. Konstandilaki, “On some properties weaker than S-closed,”
Mathematica Japonica, vol. 46, no. 2, pp. 297?304, 1997.

locally peripherally bicompact
http://books.google.co.jp/books?id=YTCKXlxkXyMC&pg=PA90&lpg=PA90&dq=peripherally+bicompact&source=bl&ots=9VG0wAfbU3&sig=2aOHqpIejrhEYdQdAQ480OJp1vQ&hl=ja&ei=_-18TM3jNtePcNTdiKcF&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCQQ6AEwAw#v=onepage&q=peripherally%20bicompact&f=falsehttp://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pjm/1103033796

stably compact(bitopologyの用語でない)
http://downloads.hindawi.com/journals/ijmms/2005/367623.pdf p.2422

(1,2)^*-sgo-comapct
http://www.m-hikari.com/ijcms-2010/9-12-2010/parkunanIJCMS9-12-2010.pdf
たぶんBitopologyの用語

MR0493976 (58 #12927)
Sharma, P. L.; Namdeo, R. K.
On nearly-isocompact spaces.
Ann. Soc. Sci. Bruxelles Sér. I 91 (1977), no. 3, 127--130.

isonearly compact
nearly countably compact
CL-isonearly compact
hereditarily isocompact
hereditarily CL-isonearly compact
http://atlas-conferences.com/cgi-bin/abstract/select/caeu-01

feebly s-compact
http://atlas-conferences.com/c/a/e/h/40.htm

hereditarily σ-metacompact
a topological space X is called hereditarily σ-metacompact if and only if every subspace A in X is σ-metacompact

1^*-subparacompact
http://www.cnki.com.cn/Article/CJFD2005-SDXK200503020.htm

convergenceのcompactnessという性質がある。
Frédéric Mynard, First-Countability, Sequentiality and Tightness of the Upper Kuratowski Convergence, http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181069940.

\mathfrak{J}-compact
\mathfrak{J}-compactoid
locally compact
locally hereditarily compact
(□,■)-compact???
quasi ideal-cover-compact
quasi countably ideal-cover-compact
core-compact

monocompactnessはtopological ringに対しても定義されている。
M. I. Ursul, Locally Compact Topologically Nil and Monocompact PI-rings, http://www.emis.ams.org/journals/BAG/vol.42/no.1/b42h1urs.pdf.

↓C-compactの別の定義が載っているっぽい。nearly c-compactも載っているっぽい。
P.L. Sharma and R.K. Namdeo,
On nearly C-compact spaces,
Anna. Dela Sci. de Bruxells, Tome 91,II (1977), 72-75.

適当に羅列

見かけたコンパクトをとりあえず片っ端から羅列しましょう。
だいたいアルファベット順。

almost base-compact?
almost λ-compact?
adequate compact?
anti φ-compact?
assymetrically compact?
base metacompact?
base hypocompact?
base ultraparacompact?
base-cover ultraparacompact?
boundedly ι-compact
B-compact?
boundedly compact? ・・・・ every closed bounded set in (X, d) is compact
c^{\mathcal{F}}-compact
c-paracompact?
countably regularly co-compact?
d-paracompact?
doubly hereditarily precompact?
epicompact?
\mathcal{F}-[μ、λ]-compact
\mathcal{F}-D-compact
\mathcal{F}-compact （フォントが違うかも）
finally λ-compact
G-compact?
gsC-compact?
Hausdorff compact?
hereditarily compact?
hereditarily iso-nearly compact?
hereditarily realcompact?
hereditarily σ-metacompact?
hsg-compact?
hereditarily weakly submetacompact?
iso-nearly compact?
initally < λ compact
initially m-chain compact
initially m-compact
finally λ-compact
fully paracompact?
locally bicompact?
locally countably compact?
locally pseudocompact?
locally semi θ-compact
maximally semi-compact?
measure compact?
monotonically ultraparacompact?
monotonically countably paracompact?
monocompact?
maximally compacnearly finally compact?
movable compact?
M-compact?
M-pseudocompact?
\mathfrak{M}-compact
maximally compact?
nearly c-compact?
nowhere locally pseudocompact?
order paracompact?
PF-compact?
preferably compact?
ponomarev bicompact?
quasi-p-pseudocompact?
quasi-p-compact?
quasi-M-compact?
regular supercompact?
subhypocompact?
selfcompact?
strictly quasi-paracompact?
strongly quasi-paracompact?
strongly nearly compact?
semi θ-compact?
sgp-compact? (semi generalized precompact??)
totally Φ-compact?
totally initially m-compact?
totally ultraparacompact?
totally hypocompact?
totally compact?
usco-compact? (E p461)
weakly anti-compact?
weakly λ-?_0-compact?
weakly λ-compact?
weakly submesocompact?
α-submetacompact?
σ-quasi-p-pseudocompact?
σ-p-compact?
σ-countably compact?
Φ-compact?
θ-(m, n)-compact?
κ-compact?
ι-compact?
\Lambda_s-compact
\mathfrac{O}-(μλ)-compact

Topological spaceの性質じゃない"かも"しれない"Compact"

Kuratowski-compact
k-compact
core-compact
T-core-compact
countably core-compact
ξ-compact
Sξ-compact
ξ-\mathbb{D}-compact
Adh_{\mathbb{D}}ξ-\mathbb{D}-compact
\mathbb{D}-selfcompact
\mathbb{F}_1-compact
ξ-\mathbb{F}_1-compact
\mathbb{H}-compact

τ -compact
hypercompact

cover compact
σ-cover compact

ρ-compact

恐らくTopological spaceの性質ではない"Compact"

c-compact (C-compactとは別 cは恐らくcategorically)
c^{B}-compact

κ-compact　(logicの用語?にもあるぽい)
(κ,κ)-compact
weakly κ-compact
fully compact
?_0-compact

hereditarily collectionwise Hausdorff compact

random compact
c-compact
c'-compact
compactoid
local compactoid
pure compactoid
KM-compactoid
k-compact
H-compact
wp-compact
wm-compact

sm-compact
strongly \aleph_0 comapct
countably strong Lowen's compact

用語の約束（案）

  • regularはT_1を含め、T_3はT_1を含めない。
  • completely regularとTychonoffは同義でありT_1を含め、 imgtex.fcgi?%5bres=100%5d%7b$T_%7b3%5cfrac%7b1%7d%7b2%7d%7d$%7d%25.png はT_1を含めない。
  • normalはT_1を含め、T_4はT_1を含めない。
  • completely normalとhereditarily normalは同義でありT_1を含め、T_5はT_1を含めない。
  • perfectly normalはT_1を含め、T_6はT_1を含めない。
  • neighberhoodはopenであることを含めない。
  • compactはT_2を含めない。
  • k-spaceはT_2を含めない。
  • paracompactはT_2を含めない。
  • open (closed) mapはcontinuousであることを含めない(?)。
  • locally convex spaceはT_2であることを含める。
  • topological groupはT_2であることを含めない(?)。
  • locally compact groupはT_2であることを含める(?)。
  • topological manifoldはsecond countableであることを含めない。
  • 部分集合族のrefinementは各族がcoveringであることを含めない。
  • compactificationはT_2であることを含める(?)。