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* ID :  [https://www.wikidata.org/wiki/Q4720484 Q4720484]

2020년 12월 26일 (토) 05:05 판

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말뭉치

  1. Pontryagin theorem; the duality formulated in it is known as Alexander–Pontryagin duality or as Pontryagin duality.[1]
  2. In mathematics, Alexander duality refers to a duality theory presaged by a result of 1915 by J. W. Alexander, and subsequently further developed, particularly by Pavel Alexandrov and Lev Pontryagin.[2]
  3. Alexander had little of the modern apparatus, and his result was only for the Betti numbers, with coefficients taken modulo 2.[2]
  4. In the process, we develop coarse topological language and a formulation of coarse Alexander duality which is suitable for applications involving quasi-isometries and geometric group theory.[3]
  5. (2) a refinement of the Borel--Moore homology of the coverage gaps with a positive cone encoding time orientation, and (3) a positive variant of Alexander Duality.[4]
  6. This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions.[5]
  7. The class of simplicial complexes representing triangulations and subdivisions of Lawrence polytopes is closed under Alexander duality.[6]
  8. The aim of the present article is to make a survey and prove the main results which are necessary for a proof of the generalization of Alexander duality theorem of W.S. Massey.[7]
  9. In this paper we introduce a relative version of this Čech homology that satisfies the Eilenberg-Steenrod Exactness Axiom, and we prove a relative version of coarse Alexander duality.[8]
  10. We show that the basis for the complementary fraction is the Alexander dual of the first basis, constructed by shifting monomial exponents.[9]
  11. This map is an isomorphism and it is called the Alexander-Čech duality (or sometimes simply Alexander duality).[10]
  12. This paper extends Alexander Duality to this setting.[11]
  13. Com binato ria l Alexander dualit y exis ts in more general ve rsions.[12]

소스

  1. ↑ Encyclopedia of Mathematics
  2. ↑ 2.0 2.1 Alexander duality
  3. ↑ Kapovich , Kleiner : Coarse Alexander duality and duality groups
  4. ↑ Positive Alexander Duality for Pursuit and Evasion
  5. ↑ Proceedings of the twenty-eighth annual symposium on Computational geometry
  6. ↑ Alexander duality in subdivisions of Lawrence polytopes
  7. ↑ On the Alexander duality theorem
  8. ↑ Coarse Alexander duality for pairs and applications
  9. ↑ Alexander duality in experimental designs
  10. ↑ Alexander-Čech duality in nLab
  11. ↑ HHA vol. 15 (2013) no. 2 article 14
  12. ↑ (PDF) Note: Combinatorial Alexander Duality

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