Abstract
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of bounded group homomorphisms are established.
Highlights
Necessary and sufficient conditions for the exactness of certain sequences of bounded group homomorphisms are established
Let us show the exactness of the sequence
The strictness of u is essential for the validity of the implication (a) ⇒ (b) in Theorem 3.1, as we shall see in the following
Summary
Abstract: Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of bounded group homomorphisms are established. The following conditions are equivalent: (a) u is strict and the sequence e → B −u→ C −v→ D Of group homomorphisms is exact; (b) for each bornological group (H, H), the sequence e → Homb((H, H), (B, B)) −u→∗ Homb((H, H), (C, C)) −v→∗ Homb((H, H), (D, D))
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