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homological complex of topological vector spaces (Definition)
Definition 0.1   A homological complex of topological vector spaces is a pair $(E_{\bullet}, d)$, where $E_{\bullet} = (E_q)_{q \in Z}$ is a sequence of topological vector spaces and $d = (d_q)_{q \in Z}$ is a sequence of continuous linear maps $d_ q$ from $E_{q+1}$ into $E_q$ which satisfy $d_q \circ d_{q+1} = 0$.

Remarks

  • The homological complex of topological vector spaces is a specifc example of a chain complex.
  • A sequence of $R$-modules and their homomorphisms is said to be a $R$-complex.



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Keywords:  homological complex of topological vector spaces

Cross-references: homomorphisms, vector spaces, topological
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This is version 1 of homological complex of topological vector spaces, born on 2009-02-16.
Object id is 530, canonical name is HomologicalComplexOfTopologicalVectorSpaces.
Accessed 490 times total.

Classification:
Physics Classification: 00. (GENERAL)
 03.65.Fd (Algebraic methods )
Pending Errata and Addenda
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