On \(\alpha\)-layer ideal topologies (Q446393)

Summary: The purpose of this paper is to study the theory of two different kinds of \(\alpha\)-layer order-preserving operator spaces, namely, \(\omega_\alpha\)-\textit{opos} and \(\omega^\ast_\alpha(\Im)\)-\textit{opos}. The former kind of space is formed by \(\alpha\)-layer functions in \(L\)-fuzzy order-preserving operator spaces. The latter kind of space is derived by local \(\alpha\)-remote neighborhood functions, which are related with \(\omega_\alpha\)-\textit{opos} and \(\alpha\)-ideals. We study characteristic properties of the two kinds of spaces, respectively, and give some applications to show the intimate relations under two different \(\omega^\ast_\alpha(\Im)\)-\textit{opos}s.