Geodesic
Pseudometrics on Ext-semigroups
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 435-451 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper considers certain pseudometric structures on Ext-semigroups and gives a unified characterization of several topologies on Ext-semigroups. It is demonstrated that these Ext-semigroups are complete topological semigroups. To this end, it is proved that a metric induces a pseudometric on a quotient space with respect to an equivalence relation if it has certain invariance. We give some properties of this pseudometric space and prove that the topology induced by the pseudometric coincides with the one induced by the quotient map.
This paper considers certain pseudometric structures on Ext-semigroups and gives a unified characterization of several topologies on Ext-semigroups. It is demonstrated that these Ext-semigroups are complete topological semigroups. To this end, it is proved that a metric induces a pseudometric on a quotient space with respect to an equivalence relation if it has certain invariance. We give some properties of this pseudometric space and prove that the topology induced by the pseudometric coincides with the one induced by the quotient map.
DOI : 10.21136/CMJ.2019.0352-18
Classification : 22A05, 46L05
Keywords: pseudometric; topological group; extension; Ext-group 
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Wei, Changguo; Zhao, Xiangmei; Liu, Shudong. Pseudometrics on Ext-semigroups. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 435-451. doi: 10.21136/CMJ.2019.0352-18

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