| The Special Singular Indexes of -spaces as Invariant Quanta of -Homotopy-types of ■-spaces |
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| 引用本文： | 张增喜.The Special Singular Indexes of -spaces as Invariant Quanta of -Homotopy-types of ■-spaces[J].东北数学,1999(3). |
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| 作者姓名： | 张增喜 |
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| 作者单位： | Department of Mathematics,Capital Normal University,Beijing,100037 |
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| 摘 要： | In1j,theautherdefinedtheconceptof"specialindex"bythetoolthatissingularcohomologywithSmith-periodictransformationforarc-connectedHausdorffspaces.ThisconceptplaysacrucialroleinthestudyofB.Knasterconjecture.Inthispaper,wefirstdefinetheconceptof"specialsingularindex"corresp0ndingtothe"specialindex"byCech-cohomologywithSmithperi0dictransformationfor'X-compactconnectedHausd0rffspaces(seetheendof51..))andintroducetheconceptsofgr-map,X-homotopiesbetween.r-maps,X-homot0py-equivalentsbetweenx-space…
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| 关 键 词： | ■-map ■-homotopy ρ′-cohomoloty Sequence ρ′-boundary Homeomorphism Special Singular Index |
The Special Singular Indexes of spaces as Invariant Quanta of Homotopy-types of spaces |
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| Zhang Zengxi.The Special Singular Indexes of spaces as Invariant Quanta of Homotopy-types of spaces[J].Northeastern Mathematical Journal,1999(3). |
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| Authors: | Zhang Zengxi |
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| Abstract: | In this paper, we introduce the concepts of map, homotopies between maps, homotopy-equivalents between spaces etc. and define the concept of special singular index of space by Cech-Smith special singular cohomology theory for compact connected Hausdorff space.Furthermore, we prove that the special singular indexes of spaces are the lnvariant quanta for homotopy-types of spaces. Consequently, they are the invariant quanta for homeomorphism-types of space, too. |
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