On the embedding of convex spaces in stratified L-convex spaces
نویسندگان
چکیده
Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the category SL-CS as a coreflective subcategory when L satisfying a multiplicative condition. By comparing the two functors and the well known Lowen functor (between topological spaces and stratified L-topological spaces), we exhibit the difference between (stratified L-)topological spaces and (stratified L-)convex spaces.
منابع مشابه
Category and subcategories of (L,M)-fuzzy convex spaces
Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...
متن کاملFuzzy convergence structures in the framework of L-convex spaces
In this paper, fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the category of $L$-con...
متن کاملCharacterizations of $L$-convex spaces
In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...
متن کاملL-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS
The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.
متن کاملOn the dual of certain locally convex function spaces
In this paper, we first introduce some function spaces, with certain locally convex topologies, closely related to the space of real-valued continuous functions on $X$, where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.
متن کامل