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.

中文翻译：

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Ext-半群的伪计量学

本文考虑了 Ext-semigroups 上的某些伪度量结构，并给出了 Ext-semigroups 上几种拓扑的统一表征。证明这些Ext-半群是完备的拓扑半群。为此，证明了一个度量如果具有一定的不变性，则关于等价关系的商空间上的伪度量。我们给出了这个伪度量空间的一些性质，并证明了由伪度量引入的拓扑与由商映射引入的拓扑一致。