In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the ...In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.展开更多
Recently,crystalline porous materials such as metal-organic frameworks（MOFs）and covalent organic frameworks（COFs）have attracted much interest not only in chemistry but also in materials science due to their tunabl...Recently,crystalline porous materials such as metal-organic frameworks（MOFs）and covalent organic frameworks（COFs）have attracted much interest not only in chemistry but also in materials science due to their tunable structures and functional channels.They have some inherent disadvantages of being difficult to solution process and recovery,which might limit their wide usage.展开更多
文摘In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.
文摘Recently,crystalline porous materials such as metal-organic frameworks（MOFs）and covalent organic frameworks（COFs）have attracted much interest not only in chemistry but also in materials science due to their tunable structures and functional channels.They have some inherent disadvantages of being difficult to solution process and recovery,which might limit their wide usage.
