Keywords
- Chain Complex
- Cohomology Group
- Duality Theorem
- Compact Hausdorff Space
- Natural Homomorphism
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P.S. Alexandroff, Untersuchungen über Gestalt und Lage abgeschlossener Mengen beliebiger Dimension, Ann.Math. 30(1929), 101–187.
_____, On the homological properties of position of complexes and closed sets (Russian), Izv. Akad. Nauk SSSR Mat. Ser. 6 (1942), 227–282.
_____, The main duality theorems for non-closed sets of the n-dimensional space (Russian), Mat.Sb. 21(63), No 2(1947), 161–232.
_____, The Combinatorial topology of non-closed sets (Russian), Mat.Sb. 33(75), No 2 (1953), 241–260.
_____, Topological duality theorems, I and II (Russian), Trudy Mat.Inst. Steklov, 48 (1955) and 54 (1959).
A. Borel and J.C. Moore, Homology theory for locally compact spaces, Michigan Math. J. 7(1960), 137–159.
G.E. Bredon, Sheaf theory, Mc Graw-Hill, New York, 1967.
G.S. Čogošvili, On the homological approximations and duality theorems for arbitrary sets (Russian), Mat.Sb. 28 (70) (1951), 89–118.
R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958.
S.T. Hu, Theory of Retracts, Wayne State Univ.Press, Detroit, 1965.
Ju.T. Lisica, Duality theorems and dual shape and coshape categories (Russian), Dokl.Akad.Nauk SSSR 263(1982), 532–536.
Ju.T.Lisica, Coherent homology, cohomology and the Alexader-Pontryagin duality theorem (Russian), The 5-th Tiraspol Symp. on General Topology and its Applications, Kishiniov (1985), 139–142.
Ju.T. Lisica and S. Mardešić, Steenrod-Sitnikov homology for arbitrary spaces, Bull.Amer.Math.Soc. 9 (1983), 207–210.
_____, Strong homology of inverse systems of spaces I, Topology and its Appl. 19 (1985), 29–43.
_____, Strong homology of inverse systems III, Topology and its Appl. 20(1985), 29–31.
_____, Coherent prohomotopy and strong shape, Glasnik Mat. 19 (39)(1984), 335–399.
_____, Coherent prohomotopy and strong shape for pairs, Glasnik Mat. 20 (40)(1985), 419–434.
_____, Steenrod homology, Geometric and algebraic topology, Banach Center Publ. 18(1986), Warsaw, 333–347.
S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibration, Fund.Math. 114(1981), 53–78.
_____, On resolutions for pairs of spaces, Tsukuba J.Math. 8 (1984), 81–93.
S. Mardešić and J. Segal, Shape theory, North-Holland, Amsterdam, 1982.
E.F. Miščenko, On some questions of combinatorial topology of non-closed sets (Russian). Mat.Sb. 32 (74) (1953), 219–224.
K. Morita, Čech cohomology and covering dimension for topological spaces, Fund.Math. 87 (1975), 31–52.
B.A. Pasynkov, On the extension of continuous maps (Russian), Dokl.Akad.Nauk SSSR, 219, No 1 (1974), 39–42.
T. Porter, Coherent prohomotopical algebra, Cahiers Topologie et Géometrie Différentielle, 18 (1977), 139–179.
F. Raymond, Local cohomology groups with closed supports, Math.Z. 76(1961), 31–41.
K.A. Sitnikov, Duality law for non-closed sets (Russian), Dokl. Akad.Nauk SSSR 81 (1951), 359–362.
_____, Combinatorial topology of non-closed sets I and II (Russian), Mat.Sb. 34(76)(1954), 3–54 and 34(79)(1955), 385–434.
E.G. Skljarenko, On the theory of generalized manifolds (Russian) Izv.Akad.Nauk SSSR Ser.Mat. 35 (1971), 831–843(Mat.USSR Izvestija 5(1971), 845–857).
E.G. Skljarenko, Homology theory and the exactness axiom (Russian) Uspehi Mat.Nauk 24(1969), No 5, 87–140.
_____, On the homology theory associated with the Alexanddroff-Čech cohomology (Russian), Uspehi Mat.Nauk 34(1979), No 6, 90–118.
E.H.Spanier, Algebraic Topology, Springer-Verlag, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Lisica, Y.T. (1987). The alexander-pontryagin duality theorem for coherent homology and cohomology with coefficients in sheaves of modules. In: Mardešić, S., Segal, J. (eds) Geometric Topology and Shape Theory. Lecture Notes in Mathematics, vol 1283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081425
Download citation
DOI: https://doi.org/10.1007/BFb0081425
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18443-0
Online ISBN: 978-3-540-47975-8
eBook Packages: Springer Book Archive
