Quasinorms and norms on topological algebraic systems (Q2719472)
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scientific article; zbMATH DE number 1609713
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasinorms and norms on topological algebraic systems |
scientific article; zbMATH DE number 1609713 |
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25 June 2001
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0.90489817
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0.88699037
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0.8823137
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Quasinorms and norms on topological algebraic systems (English)
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This paper continues the authors' investigations [ibid. 2, No. 1, 10-20 (1995; Zbl 0964.54028), see above]. The authors study the properties of quasinormed and normed topological algebraic systems which are generalizations of topological groups. It is established that the necessary existence condition on the topological algebraic system for a family of quasinorms (norms) which determines the topology of this system is the multiplicative (strong multiplicative) complete regularity of the topological algebraic system. The relationships between the classes of the multiplicative totally regular, strong multiplicative totally regular, quasinormed and normed topological algebraic systems are studied.
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