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Relative torsion theories for the category of separable, locally convex spaces. (Russian) Zbl 0614.46061

This installment, continuing from ibid. 85, 43-57 (1985; Zbl 0594.54024), asks: given a completion P and an adjoint pair of subcategories K,R with coreflector k and reflector r, when is (K,P) a relative torsion theory? (in separated locally convex spaces).
The main result is that this is equivalent to \(kp=pk\) or to \(rp=pr\).
Reviewer: J.R.Isbell

MSC:

46M15 Categories, functors in functional analysis
18E40 Torsion theories, radicals
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18A35 Categories admitting limits (complete categories), functors preserving limits, completions

Citations:

Zbl 0594.54024
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