Characteristic values of T-filters
Let \((L, \leq, *)\) be a complete MV-algebra, \(X\) be a set. A \(\top\)-filter on \(X\) is a subset of \(L^X\) with certain conditions and an \(L\)-filter on \(X\) is a function \(L^X\longrightarrow L\) with certain conditions. Both \(\top\)-filter and \(L\)-filter can be employed to establish convergence theories in \(L\)-topological spaces. In this paper, the authors extend the notion of characteristic value for prefilters introduced in [\textit{R. Lowen}, General Topology Appl. 10, 147-160 (1979; Zbl 0409.54008)] to every subset of \(L^X\), and then obtain a simple postulation of \(\top\)-filters. The interesting relationship among \(\top\)-filters, \(L\)-filters, and \(L\)-filters of ordinary sets is also discussed.
scientific article; zbMATH DE number 5001335
scientific article