ω-Convergence theory of filters in Lω-spaces

摘要

In this paper, an ω-convergence theory of filters in an Lω-space is established. By means of the ω-convergence theory, some important characterizations with respective to the ω-closed sets, ωT{sub}2 separation and (ω{sub}1, ω{sub}2)-continuous mappings are obtained. Moreover, the mutual relationships among ω-convergence of molecular nets, ω-convergence of ideals and ω-convergence of filters are given.