On G-quotient Mappings and Networks Defined by G-convergence  

作　　者：Fang Liu Xiangeng Zhou Li Liu 

机构地区：[1]Department of Mathematics,Ningde Normal University,Ningde 352100,China

出　　处：《Journal of Mathematical Study》2023年第2期135-146,共12页数学研究（英文）

基　　金：supported by Natural Science Foundation of Fujian Province(Grant No.2020J01428);Educational Research Projects of Middle-aged Teachers of Fujian Province(Grant No.JAT200685).

摘　　要：Let G_(1),G_(2) be methods on topological spaces X and Y respectively,f:X→Y be a mapping,P be a cover of X.f is said to be a(G_(1),G_(2))-quotient mapping provided f^(−1)(U)is G_(1)-open in X,then U is G_(2)-open in Y.P is called a G-cs′-network of X if whenever x={xn}n∈N∈cG(X)and G(x)=x∈U with U open in X,then there exists some n0∈N such that{x,x_(n0)}⊂P⊂U for some P∈P.P is called a G-kernel cover of X if{(U)_(G):U∈P}is a cover of X.In this paper,we introduce the concepts of(G_(1),G_(2))-quotient mappings,G-cs′-networks and G-kernel covers of X,and study some characterizations of(G_(1),G_(2))-quotient mappings,G-cs′-networks,and G-kernel covers of X.In particular,we obtain that if G is a subsequential method and X is a G-Fréchet space with a point-countable G-cs′-network,then X is a meta-Lindelöf space.

关 键 词：G-methods G-convergence G-quotient mappings G-cs′-networks G-kernel covers G-Fréchet spaces 

分 类 号：O189[理学—数学]