PlanetMath: variable network topology

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variable network topology

(Definition)

Definition 0.1 A variable network topology is defined by an indexed family or class of networks of one-dimensional

-complexes

with $i \in I$ in the category Top of topological spaces with additional homology (or cohomology) axioms, rules, or properties of the underlying

-complexes, that specify the transformation maps as a sequence of homotopoy maps.

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"variable network topology" is owned by bci1.

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See Also: supercategory, $CW$

Other names:

variable network topology

Also defines:

sequence of different network topologies, esp. connectivities

Keywords:

sequence of different network topologies defined by distinct axioms or rules

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Cross-references: sequence, maps, transformation, properties, axioms, cohomology, homology, topological spaces, category, class
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This is version 5 of variable network topology, born on 2008-07-24, modified 2008-10-18.
Object id is 10859, canonical name is VariableTopology3.
Accessed 384 times total.

Classification:

AMS MSC:	18B40 (Category theory; homological algebra :: Special categories :: Groupoids, semigroupoids, semigroups, groups )
	18G55 (Category theory; homological algebra :: Homological algebra :: Homotopical algebra)
	55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory)
	55U35 (Algebraic topology :: Applied homological algebra and category theory :: Abstract and axiomatic homotopy theory)
	55U05 (Algebraic topology :: Applied homological algebra and category theory :: Abstract complexes)

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