Simultaneously reflective and coreflective full subconstructs of stratified L-topological spaces are concretely reflective and coreflective

✍ Scribed by Dexue Zhang

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 223 KB
• Volume: 144
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(03)00299-9

✦ Synopsis

Let L be a completely distributive lattice. A stratiÿed L-topology on a set X is a subfamily of L-subsets of X which is closed with respect to arbitrary suprema and ÿnite inÿnima, and contains all the constants. In this paper, it is shown that every simultaneously re ective and core ective full subconstruct of stratiÿed L-topological spaces is necessarily concretely re ective and core ective. In other words, every such subconstruct is necessarily both initially and ÿnally closed. As an application, it is demonstrated that the construct of bitopological spaces has exactly 4 simultaneously re ective and core ective full subconstructs.