\(\omega \)-convergence theory of filters in \(L\omega \)-spaces (Q839470)

In this paper, an \(\omega \)-convergence theory of filters in an \(L\omega\)-space is established. By means of this convergence theory, some important characterizations with respect to \(\omega \)-closed sets, the \(\omega T_2\) separation axiom and \((\omega_1, \omega_2)\)-continuous mappings are obtained. Moreover, the relationships between \(\omega \)-convergence of molecular nets, \(\omega \)-convergence of ideals and \(\omega \)-convergence of filters are given.