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gptkbp:instanceOf
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Homology Theory
|
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gptkbp:appliesTo
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All Topological Spaces
|
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gptkbp:basisFor
|
Singular Chains
|
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gptkbp:category
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gptkb:Mathematics
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gptkbp:computes
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Topological Invariants
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gptkbp:field
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gptkb:Algebraic_Topology
|
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gptkbp:generalizes
|
Simplicial Homology
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https://www.w3.org/2000/01/rdf-schema#label
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Singular Homology Theory
|
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gptkbp:introduced
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gptkb:Eilenberg
gptkb:Steenrod
|
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gptkbp:output
|
Homology Groups H_n(X)
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gptkbp:provides
|
Homology Groups
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gptkbp:relatedTo
|
gptkb:Alexander_Duality
gptkb:Betti_Numbers
gptkb:CW_Complexes
gptkb:Cellular_Homology
gptkb:De_Rham_Cohomology
gptkb:Excision_Theorem
gptkb:Künneth_Theorem
gptkb:Mayer–Vietoris_Sequence
gptkb:Poincaré_Duality
gptkb:Sheaf_Cohomology
gptkb:Simplicial_Complexes
gptkb:Universal_Coefficient_Theorem
Functoriality
Algebraic Invariants
Chain Homotopy
Chain Map
Cohomology Theory
Exact Sequences
Fundamental Group
Homological Algebra
Homotopy Groups
Homotopy Invariance
Homotopy Theory
Reduced Homology
Relative Homology
Spectral Sequences
Topological Invariants
|
|
gptkbp:satisfies
|
gptkb:Eilenberg–Steenrod_Axioms
|
|
gptkbp:studies
|
Topological Spaces
|
|
gptkbp:usedFor
|
Classifying Spaces
Detecting Holes in Spaces
|
|
gptkbp:uses
|
Abelian Groups
Boundary Maps
Boundary Operators
Chain Complexes
Free Modules
Singular Simplices
|
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gptkbp:bfsParent
|
gptkb:William_S._Massey
|
|
gptkbp:bfsLayer
|
6
|