Sober Approach Spaces are Firmly Reflective for the Class of Epimorphic Embeddings |
| |
Authors: | A Gerlo E Vandersmissen C Van Olmen |
| |
Institution: | (1) VUB – DWIS, Pleinlaan 2, Brussels, 1050, Belgium |
| |
Abstract: | In 2] the subconstruct of sober approach spaces was introduced and it was shown to be a reflective subconstruct of the category of approach spaces. The main result of this paper states that moreover is firmly -reflective in for the class of epimorphic embeddings. ‘Firm -reflective’ is a notion introduced in 3] by G.C.L. Brümmer and E. Giuli and is inspired by the exemplary behaviour of the usual completion in the category of Hausdorff uniform spaces with uniformly continuous maps. It means that is -reflective in and that the reflector is such that belongs to if and only if is an isomorphism. Firm -reflectiveness implies uniqueness of completion in the sense that whenever is a map with and sober, the associated is an isomorphism. Our result generalizes the fact that in the category the subconstruct of sober topological spaces is firmly reflective for the class of b-dense embeddings in . Also firmness in some other subconstructs of will be easily obtained.A. Gerlo and C. Van Olmen are research assistants at the Fund of Scientific Research Vlaanderen (FWO). E. Vandersmissen is a research assistant supported by the FWO-grant G.0244.05. |
| |
Keywords: | sober approach spaces approach frames firm reflections |
本文献已被 SpringerLink 等数据库收录! |