(untitled)
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={x_n}_nN c_G(X) and G(x)=xU with U open in X, then there exists some n_0N such that {x ,x_n_0 }P U for some PP. P is called a G-kernel cover of X if {(U)_G:UP} 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. , number=2, journal=Journal of Mathematical Study, year=2023, month=Jun., pages=135–146