Epireflections in the category of $T_{0}$ stratified Q-cotopological spaces

Abstract

In this paper, we show that the category SobQ-CTop of all sober Q-cotopological spaces is the epireflective subcategory of ${{\textbf {S}}}Q{\text {-}}{{\textbf {CTop}}}_{0}$ of all $T_{0}$ stratified Q-cotopological spaces. In particular, we mainly prove that ${{\textbf {Sob}}}Q{\text {-}}{{\textbf {CTop}}}$ is the epireflective hull of Sierpinski Q-cotopological space $Q_{S}$ in ${{\textbf {S}}}Q{\text {-}}{{\textbf {CTop}}}_{0}$, where Q is the unit interval endowed with a left continuous t-norm.