Some three-space properties of semitopological and paratopological groups

Piyu Li,Lei Mou,Hanfeng Wang,Li-Hong Xie

doi:10.1016/j.topol.2019.05.002

Some three-space properties of semitopological and paratopological groups

Piyu Li, Lei Mou + Show 2 more

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https://doi.org/10.1016/j.topol.2019.05.002

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Journal: Topology and its Applications	Publication Date: May 8, 2019
Citations: 3	License type: publisher-specific-oa

Affiliation: Northeastern University, Capital Normal University, Shandong Agricultural University, Wuyi University

#Paratopological Groups #Canonical Quotient Mapping + Show 8 more

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Abstract

In this paper, some three-space properties of semitopological and paratopological groups are considered. We show that: (1) if the closed invariant subgroup H of semitopological group G and the natural quotient group G/H have Gδ-diagonals, then G has a Gδ-diagonal; (2) if H is a compact invariant subgroup of paratopological group G, then the canonical quotient mapping from G to G/H is closed. An example is given to show that the result (2) can not be generalized to quasitopological groups.

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