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Epireflections in the category of \(T_{0}\) stratified Q-cotopological spaces


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.

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This research is supported by a grant of National Natural Science Foundation of China (11531009).

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BZ helped in formal analysis, writing—original draft, conceptualization, writing—review & editing, methodology, supervision. YZ contributed to visualization, writing—original draft, formal analysis, writing—review & editing, methodology, validation.

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Correspondence to Yujing Zhang.

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Zhao, B., Zhang, Y. Epireflections in the category of \(T_{0}\) stratified Q-cotopological spaces. Soft Comput 27, 2443–2451 (2023).

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  • Epireflective hull
  • Sobriety
  • Q-cotopological space
  • Sierpinski Q-cotopological space