Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 435-451, 2020
Pseudometrics on Ext-semigroups
Changguo Wei, Xiangmei Zhao, Shudong Liu
Received July 29, 2018. Published online December 10, 2019.
Abstract: 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.
Affiliations: Changguo Wei (corresponding author), Xiangmei Zhao, School of Mathematical Sciences, Ocean University of China, 238 Songling Road, Qingdao, 266100, P. R. China, e-mail: firstname.lastname@example.org, email@example.com; Shudong Liu, School of Mathematical Sciences, Qufu Normal University, 57 Jingxuan West Road, Qufu, Shandong, 273165, P. R. China, e-mail: firstname.lastname@example.org