A simplification of the Eilenberg-Steenrod axioms for finite simplicial complexes (Q1112377)
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scientific article; zbMATH DE number 4078256
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simplification of the Eilenberg-Steenrod axioms for finite simplicial complexes |
scientific article; zbMATH DE number 4078256 |
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A simplification of the Eilenberg-Steenrod axioms for finite simplicial complexes (English)
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1988
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It is shown that the familiar Eilenberg-Steenrod axioms for homology may be simplified, in the case of finite simplicial complexes, by replacing the homotopy and dimension axioms by a strengthened form of the dimension axiom asserting that every simplex (rather than a point) has homology group \({\mathbb{Z}}\) in dimension 0 and 0 in all other dimensions.
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homology groups of a simplex
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homotopy axiom
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Eilenberg-Steenrod axioms for homology
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simplicial complexes
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dimension axiom
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