Abstract
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.
Highlights
Abstract convexity theory is an important branch of mathematics (Van De Vel 1993)
The second functor enables us to prove that the category CS can be embedded in the category SL-CS as a coreflective subcategory when the continuous lattice L satisfying a multiplicative condition
When L being a continuous lattice, an embedding functor from the category CS to SLCS is introduced, it is used to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory
Summary
Abstract convexity theory is an important branch of mathematics (Van De Vel 1993). The notion of convexity considered here is considerably broader the classical one; specially, it is not restricted to the context of vector spaces. A convexity on a set is a family of subsets closed for intersection and directed union. It is seen that there is some similarity between convexity and topology (a family of subsets of a set closed for union and finite intersection).
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call