Pseudometrics on Ext-semigroups

Changguo Wei; Xiangmei Zhao; Shudong Liu

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 2, page 435-451
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Wei, Changguo, Zhao, Xiangmei, and Liu, Shudong. "Pseudometrics on Ext-semigroups." Czechoslovak Mathematical Journal 70.2 (2020): 435-451. <http://eudml.org/doc/297402>.

@article{Wei2020,
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.},
author = {Wei, Changguo, Zhao, Xiangmei, Liu, Shudong},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudometric; topological group; extension; Ext-group},
language = {eng},
number = {2},
pages = {435-451},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Pseudometrics on Ext-semigroups},
url = {http://eudml.org/doc/297402},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Wei, Changguo
AU - Zhao, Xiangmei
AU - Liu, Shudong
TI - Pseudometrics on Ext-semigroups
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 2
SP - 435
EP - 451
AB - 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.
LA - eng
KW - pseudometric; topological group; extension; Ext-group
UR - http://eudml.org/doc/297402
ER -

References

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