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homological complex of topological vector spaces∗ bci1† 2013-03-22 1:29:48 Definition 0.1. A homological complex of topological vector spaces is a pair (E• , d), where E• = (Eq )q∈Z is a sequence of topological vector spaces and d = (dq )q∈Z is a sequence of continuous linear maps dq from Eq+1 into Eq which satisfy dq ◦ dq+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. ∗ hHomologicalComplexOfTopologicalVectorSpacesi created: h2013-03-2i by: hbci1i version: h40901i Privacy setting: h1i hDefinitioni h55N25i h55N99i h55R65i h55P99i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1
