Generalized stable shape and duality

In this paper we formulate and prove a generalization of the Spanier–Whitehead duality theorem in the generalized stable shape category and discuss its consequences.

Saved in:
Bibliographic Details
Published inTopology and its applications Vol. 109; no. 1; pp. 75 - 88
Main Author Miyata, Takahisa
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2001
Subjects
Compact metric space
Coshape
CW-spectrum
Duality
Shape
Stable coshape
Stable shape
CW-spectrum
Compact metric space
Shape
55P55
Coshape
54C56
55P25
Stable shape
Duality
55P42
Stable coshape
Online AccessGet full text

Cover

Abstract In this paper we formulate and prove a generalization of the Spanier–Whitehead duality theorem in the generalized stable shape category and discuss its consequences.
AbstractList In this paper we formulate and prove a generalization of the Spanier–Whitehead duality theorem in the generalized stable shape category and discuss its consequences.
Author Miyata, Takahisa
Author_xml – sequence: 1
  givenname: Takahisa
  surname: Miyata
  fullname: Miyata, Takahisa
  email: miyata@cs.sist.ac.jp
  organization: Department of Computer Science, Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi, 437-8555 Japan
BookMark eNqFj8tKAzEUhoNUcFp9BGEWLnQRPblMMlmJlFqFggt1HTLJGYyM05KMQn16p624dXP-xX_hfFMy6dc9EnLO4JoBUzfP41G0VpJdGnMFwKSk4ogUrNaGCg56Qoq_yAmZ5vwOY8poXpCLJfaYXBe_MZR5cE2HZX5zGyxdH8rwOTrD9pQct67LeParM_J6v3iZP9DV0_JxfreiXoAeqBSt8YaDFAJ8I7UCFbiqhXEYoAqOB1H5RjTgpFGCGRc8qKZiAXUFfHRnpDrs-rTOOWFrNyl-uLS1DOwO1e5R7Y7DGmP3qFaMvdtDD8fnviImm33E3mOICf1gwzr-s_ADNopbWw
CitedBy_id crossref_primary_10_1090_S0002_9939_01_05852_X
crossref_primary_10_1016_j_topol_2010_08_013
crossref_primary_10_3336_gm_49_1_14
crossref_primary_10_1007_s10958_021_05649_z
crossref_primary_10_1016_j_topol_2003_10_012
Cites_doi 10.1007/BF01223708
10.1016/0040-9383(71)90003-6
10.1112/S002557930000070X
10.2307/1970209
10.1016/0166-8641(94)00082-E
ContentType Journal Article
Copyright 2001 Elsevier Science B.V.
Copyright_xml – notice: 2001 Elsevier Science B.V.
DBID 6I.
AAFTH
AAYXX
CITATION
DOI 10.1016/S0166-8641(99)00144-3
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1879-3207
EndPage 88
ExternalDocumentID 10_1016_S0166_8641_99_00144_3
S0166864199001443
GroupedDBID --K
--M
--Z
-~X
.~1
0R~
123
186
1B1
1RT
1~.
1~5
29Q
4.4
457
4G.
5VS
6I.
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AASFE
AAXUO
ABAOU
ABFNM
ABJNI
ABMAC
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
ADIYS
ADMUD
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HVGLF
HZ~
H~9
IHE
IXB
J1W
KOM
M26
M41
MCRUF
MHUIS
MO0
N9A
NCXOZ
NHB
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
PC.
Q38
R2-
RIG
ROL
RPZ
SCC
SDF
SDG
SES
SEW
SPC
SPCBC
SSW
SSZ
T5K
TN5
WH7
WUQ
ZKB
~G-
0SF
AAXKI
AAYXX
ADVLN
AFJKZ
AKRWK
CITATION
ID FETCH-LOGICAL-c307t-43f9c9204330cb47606d26839aed05da2d35cb3b0a496319adc06b51de75022d3
IEDL.DBID ABVKL
ISSN 0166-8641
IngestDate Thu Sep 26 17:04:00 EDT 2024
Fri Feb 23 02:27:38 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Keywords CW-spectrum
Compact metric space
Shape
55P55
Coshape
54C56
55P25
Stable shape
Duality
55P42
Stable coshape
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c307t-43f9c9204330cb47606d26839aed05da2d35cb3b0a496319adc06b51de75022d3
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S0166864199001443
PageCount 14
ParticipantIDs crossref_primary_10_1016_S0166_8641_99_00144_3
elsevier_sciencedirect_doi_10_1016_S0166_8641_99_00144_3
PublicationCentury 2000
PublicationDate 2001-00-00
PublicationDateYYYYMMDD 2001-01-01
PublicationDate_xml – year: 2001
  text: 2001-00-00
PublicationDecade 2000
PublicationTitle Topology and its applications
PublicationYear 2001
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Whitehead (BIB015) 1978
Spanier, Whitehead (BIB012) 1955; 2
Henn (BIB005) 1981; 36
Lisica (BIB007) 1980
Adams (BIB001) 1971; 10
Brown (BIB002) 1962; 75
Miyata, Segal (BIB011) 1998; 92
Eilenberg, Steenrod (BIB004) 1952
Lima (BIB006) 1959; 4
Mardešić, Segal (BIB008) 1982
Dold, Puppe (BIB003) 1980
Margolis (BIB009) 1983
Switzer (BIB013) 1975
Miyata, Segal (BIB010) 1995; 63
Watanabe (BIB014) 1987; 1283
Lima (10.1016/S0166-8641(99)00144-3_BIB006) 1959; 4
Lisica (10.1016/S0166-8641(99)00144-3_BIB007) 1980
Spanier (10.1016/S0166-8641(99)00144-3_BIB012) 1955; 2
Brown (10.1016/S0166-8641(99)00144-3_BIB002) 1962; 75
Switzer (10.1016/S0166-8641(99)00144-3_BIB013) 1975
Watanabe (10.1016/S0166-8641(99)00144-3_BIB014) 1987; 1283
Miyata (10.1016/S0166-8641(99)00144-3_BIB010) 1995; 63
Mardešić (10.1016/S0166-8641(99)00144-3_BIB008) 1982
Whitehead (10.1016/S0166-8641(99)00144-3_BIB015) 1978
Eilenberg (10.1016/S0166-8641(99)00144-3_BIB004) 1952
Dold (10.1016/S0166-8641(99)00144-3_BIB003) 1980
Margolis (10.1016/S0166-8641(99)00144-3_BIB009) 1983
Adams (10.1016/S0166-8641(99)00144-3_BIB001) 1971; 10
Miyata (10.1016/S0166-8641(99)00144-3_BIB011) 1998; 92
Henn (10.1016/S0166-8641(99)00144-3_BIB005) 1981; 36
References_xml – volume: 4
  start-page: 92
  year: 1959
  end-page: 147
  ident: BIB006
  article-title: The Spanier–Whitehead duality in new homotopy categories
  publication-title: Summa Brasiliensis Math.
  contributor:
    fullname: Lima
– year: 1952
  ident: BIB004
  publication-title: Foundations of Algebraic Topology
  contributor:
    fullname: Steenrod
– year: 1975
  ident: BIB013
  publication-title: Algebraic Topology—Homotopy and Homology
  contributor:
    fullname: Switzer
– volume: 63
  start-page: 139
  year: 1995
  end-page: 164
  ident: BIB010
  article-title: Generalized stable shape and the Whitehead theorem
  publication-title: Topology Appl.
  contributor:
    fullname: Segal
– year: 1983
  ident: BIB009
  publication-title: Spectra and the Steenrod Algebra, Modules over the Steenrod Algebra and the Stable Homotopy Category
  contributor:
    fullname: Margolis
– volume: 1283
  start-page: 221
  year: 1987
  end-page: 239
  ident: BIB014
  article-title: The continuity axiom and Čech homology
  publication-title: Geometric Topology and Shape Theory
  contributor:
    fullname: Watanabe
– year: 1978
  ident: BIB015
  publication-title: Elements of Homotopy Theory
  contributor:
    fullname: Whitehead
– year: 1982
  ident: BIB008
  publication-title: Shape Theory
  contributor:
    fullname: Segal
– volume: 36
  start-page: 327
  year: 1981
  end-page: 341
  ident: BIB005
  article-title: Duality in stable shape theory
  publication-title: Arch. Math.
  contributor:
    fullname: Henn
– volume: 92
  start-page: 1
  year: 1998
  end-page: 31
  ident: BIB011
  article-title: Generalized stable shape and Brown's representation theorem
  publication-title: Topology Appl.
  contributor:
    fullname: Segal
– volume: 2
  start-page: 56
  year: 1955
  end-page: 80
  ident: BIB012
  article-title: Duality in homotopy theory
  publication-title: Mathematika
  contributor:
    fullname: Whitehead
– volume: 10
  start-page: 185
  year: 1971
  end-page: 198
  ident: BIB001
  article-title: A variant of E.H. Brown's representability theorem
  publication-title: Topology
  contributor:
    fullname: Adams
– start-page: 81
  year: 1980
  end-page: 102
  ident: BIB003
  article-title: Duality, trace and transfer
  publication-title: Proc. Internat. Conference on Geometric Topology, Warsaw, 1978
  contributor:
    fullname: Puppe
– start-page: 299
  year: 1980
  end-page: 304
  ident: BIB007
  article-title: The theory of co-shape and singular homology
  publication-title: Proc. Internat. Conference on Geometric Topology, Warsaw, 1978
  contributor:
    fullname: Lisica
– volume: 75
  start-page: 467
  year: 1962
  end-page: 484
  ident: BIB002
  article-title: Cohomology theories
  publication-title: Ann. of Math.
  contributor:
    fullname: Brown
– volume: 36
  start-page: 327
  year: 1981
  ident: 10.1016/S0166-8641(99)00144-3_BIB005
  article-title: Duality in stable shape theory
  publication-title: Arch. Math.
  doi: 10.1007/BF01223708
  contributor:
    fullname: Henn
– year: 1982
  ident: 10.1016/S0166-8641(99)00144-3_BIB008
  contributor:
    fullname: Mardešić
– volume: 4
  start-page: 92
  year: 1959
  ident: 10.1016/S0166-8641(99)00144-3_BIB006
  article-title: The Spanier–Whitehead duality in new homotopy categories
  publication-title: Summa Brasiliensis Math.
  contributor:
    fullname: Lima
– volume: 10
  start-page: 185
  year: 1971
  ident: 10.1016/S0166-8641(99)00144-3_BIB001
  article-title: A variant of E.H. Brown's representability theorem
  publication-title: Topology
  doi: 10.1016/0040-9383(71)90003-6
  contributor:
    fullname: Adams
– start-page: 299
  year: 1980
  ident: 10.1016/S0166-8641(99)00144-3_BIB007
  article-title: The theory of co-shape and singular homology
  contributor:
    fullname: Lisica
– year: 1978
  ident: 10.1016/S0166-8641(99)00144-3_BIB015
  contributor:
    fullname: Whitehead
– volume: 1283
  start-page: 221
  year: 1987
  ident: 10.1016/S0166-8641(99)00144-3_BIB014
  article-title: The continuity axiom and Čech homology
  contributor:
    fullname: Watanabe
– year: 1983
  ident: 10.1016/S0166-8641(99)00144-3_BIB009
  contributor:
    fullname: Margolis
– year: 1975
  ident: 10.1016/S0166-8641(99)00144-3_BIB013
  contributor:
    fullname: Switzer
– year: 1952
  ident: 10.1016/S0166-8641(99)00144-3_BIB004
  contributor:
    fullname: Eilenberg
– volume: 2
  start-page: 56
  year: 1955
  ident: 10.1016/S0166-8641(99)00144-3_BIB012
  article-title: Duality in homotopy theory
  publication-title: Mathematika
  doi: 10.1112/S002557930000070X
  contributor:
    fullname: Spanier
– start-page: 81
  year: 1980
  ident: 10.1016/S0166-8641(99)00144-3_BIB003
  article-title: Duality, trace and transfer
  contributor:
    fullname: Dold
– volume: 92
  start-page: 1
  year: 1998
  ident: 10.1016/S0166-8641(99)00144-3_BIB011
  article-title: Generalized stable shape and Brown's representation theorem
  publication-title: Topology Appl.
  contributor:
    fullname: Miyata
– volume: 75
  start-page: 467
  year: 1962
  ident: 10.1016/S0166-8641(99)00144-3_BIB002
  article-title: Cohomology theories
  publication-title: Ann. of Math.
  doi: 10.2307/1970209
  contributor:
    fullname: Brown
– volume: 63
  start-page: 139
  year: 1995
  ident: 10.1016/S0166-8641(99)00144-3_BIB010
  article-title: Generalized stable shape and the Whitehead theorem
  publication-title: Topology Appl.
  doi: 10.1016/0166-8641(94)00082-E
  contributor:
    fullname: Miyata
SSID ssj0001972
Score 1.6021395
Snippet In this paper we formulate and prove a generalization of the Spanier–Whitehead duality theorem in the generalized stable shape category and discuss its...
SourceID crossref
elsevier
SourceType Aggregation Database
Publisher
StartPage 75
SubjectTerms Compact metric space
Coshape
CW-spectrum
Duality
Shape
Stable coshape
Stable shape
Title Generalized stable shape and duality
URI https://dx.doi.org/10.1016/S0166-8641(99)00144-3
Volume 109
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB76uOhBfGJ9lBx60MO2SXazzR7bYmmt7UUrvS37KgYkFlsPevC3u5uktYJ4EAKBCbNkZ5lvvoGZWYCGaEtKBFUoDARBJNYBYooKJI3GWBNfGe0SxfGEDqbkdhbNStBb98K4ssoC-3NMz9C6kLQKa7YWSdK6t2SFxpQEFk9dWoDLUA0t-7XeWe10H0d3G0B2N2vlI74pcgrfjTz5IpnwirHrbB2Efw9RW2Gnvw97BV_0OvkvHUDJpIewO94MW10eQaMYHZ18GO1Zsiefjbd8EgvjiVR7OuuafD-Gaf_moTdAxeUHSFm3WyGC50wx17mKfSVJ2yYaOqSWzgij_UiLUONISSx9QawPBUxo5VMZBdpYDhDarydQSV9ScwqedK1WYSxiTd0kIxnbcBXpdmjm0VxJxWrQXO-XL_IZF3yr-ItS7gzEGeOZgTiuQby2Cv9xWNzi8N-qZ_9XPYedvADMPRdQWb2-mUvLCFayDuXmZ1Avzt29h6PBxEqHs-4XUP-xIA
link.rule.ids 315,783,787,3513,4031,4509,24128,27581,27935,27936,27937,45597,45675,45691,45886
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV09T8MwED2VMgAD4lOUzwwdYDBNYseNR0BULbRdaKVulu1zRSUUKloG-PXYSVqKhBiQMjmx5Zztd--ke2eAumpqzhQ3JI4UIyzFiAjDFdEWKUUWGos-UOz1eXvIHkbJqAJ3Cy2MT6sssb_A9Byty5ZGac3GdDJpPDmywlPOIoenPiyga7DuZZd-m3dGt0s49vdqFQW-OfGff8t4iiHyxkshrvJRCP3dQa04ndYObJdsMbgpJrQLFZvtwVZvWWp1tg_1snD05NNi4KiefrHB7FlNbaAyDDDXTH4cwLB1P7hrk_LqA2LcoZsTRsfCCK9bpaHRrOnCDIy5IzPKYpigipEmRlMdKuZOUCQUmpDrJELrGEDs3h5CNXvN7BEE2gut4lSlyH0dI506Z5VgM7bjZGy0ETW4XvyvnBYVLuRK6hfn0htICiFzA0lag3RhFfljqaRD4b-7Hv-_6wVstAe9rux2-o8nsFmkgvnnFKrzt3d75rjBXJ_na_8FLCuvZA
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Generalized+stable+shape+and+duality&rft.jtitle=Topology+and+its+applications&rft.au=Miyata%2C+Takahisa&rft.date=2001&rft.issn=0166-8641&rft.volume=109&rft.issue=1&rft.spage=75&rft.epage=88&rft_id=info:doi/10.1016%2FS0166-8641%2899%2900144-3&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_S0166_8641_99_00144_3
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0166-8641&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0166-8641&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0166-8641&client=summon