On H-sober spaces and H-sobrifications of T0 spaces

• A uniform approach to d -spaces, sober spaces and well-filtered is provided. The theory of (super) H-sober established. If H has property M, then the function space super equipped with topology pointwise convergence H-sober. a T 0 X iff its Smyth power P S ( ) category all reflective in Top . if M. In this paper, we provide spaces, develop general framework for dealing these spaces. concepts irreducible subset systems (R-subset short), R-subset system are introduced. It proved that product family each factor H-sober, natural (called M), H-sobriety special type H-sobriety, hence Let be continuous mappings. For an Y , show Furthermore, M space, One immediate corollary well-filtered. having not general. But prove direct construction H-sobrifications given. So also