On P-bases and ωω-sn-networks

In this paper, we discuss some properties of paratopological groups and coset spaces with P-bases and co omega-sn-networks, respectively. We mainly give the following results: (1) Let P = 1C(M) for a separable metric space M. If G is a Frechet-Urysohn Hausdorff paratopological group having the property (**) with a P-base, then G is first-countable, hence submetrizable; (2) Let P = 1C(M) for a separable metric space M. If H is a closed neutral subgroup of a topological group G such that G/H is a Frechet-Urysohn space with a P-base, then G/H is first-countable, hence metrizable; (3) A Frechet-Urysohn Hausdorff paratopological group G has an co omega-weak base if and only if it has an co omega-base; (4) Every Frechet-Urysohn Hausdorff paratopological group having the property (**) with an co omega-sn-network is first-countable, hence submetrizable.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we discuss the properties of paratopological groups and coset spaces with P-bases and co omega-sn-networks. We mainly focus on the first-countability and metrizability conditions of these groups and spaces.