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New Structures Based on Completions

Abstract : We propose new axioms relative to combinatorial topology. These axioms are settled in the framework of completions which are inductive properties expressed in a declarative way, and that may be combined. We introduce several completions for describing dyads. A dyad is a pair of complexes which are, in a certain sense, linked by a "relative topology". We first give some basic properties of dyads, then we introduce a second set of axioms for relative dendrites. This allows us to establish a theorem which provides a link between dyads and dendrites, a dendrite is an acyclic complex which may be also described by completions. Thanks to a previous result, this result makes clear the relation between dyads, relative dendrites, and complexes which are acyclic in the sense of homology.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00835544
Contributor : Michel Couprie <>
Submitted on : Wednesday, June 19, 2013 - 8:55:41 AM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM
Long-term archiving on: : Friday, September 20, 2013 - 4:05:16 AM

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  • HAL Id : hal-00835544, version 1

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Gilles Bertrand. New Structures Based on Completions. Discrete Geometry for Computer Imagery, Mar 2013, Spain. pp.83-94. ⟨hal-00835544⟩

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