On Q-sobriety

Abstract

The study of fixed-basis variety-based topology was initiated by S.A. Solovyov (in 2008), which, among other things, generalizes fuzzy topology. We extend within this framework, an earlier result due to Srivastava et al. (in 1998), which showed that the category of sober fuzzy topological spaces is the epireflective hull of the fuzzy Sierpinski space in the category of T₀-fuzzy topological spaces.

Mathematics Subject Classification (2010):

• 54A40
• 18Axx

Key words:

• Ω-algebra
• Q-topological space
• Q-sober topological space
• Q-T₀-topological space
• epireflective hull