On coreflective hulls in Str-Q-TOP

Abstract

Solovyov (Fuzzy Sets Syst 159:2567–2585, 2008) introduced the notion of stratified Q-topological spaces, which in turn gives rise to the category Str-Q-TOP of stratified Q-topological spaces (where Q is a fixed member of a fixed variety of $\Omega$-algebras). Singh and Srivastava (Ann. Fuzzy Math. Inform. 12:539–546, 2016) introduced the Q-topological space $(Q, \langle \{id_{Q}\}\cup \{\underline{q} \mid q\in Q\}\rangle )$ which is a Sierpinski object in the category Str-Q-TOP. In this paper, motivated by Singh (Fuzzy Sets Syst 159:2611–2615, 2008), we determine the coreflective hull of $(Q, \langle \{id_{Q}\}\cup \{\underline{q} \mid q\in Q\}\rangle )$ in the category Str-Q-TOP. We also determine the coreflective hulls of the categories Str-Dis-Q-TOP of discrete Q-topological spaces and Str-Ind-Q-TOP of stratified indiscrete Q-topological spaces, in the category Str-Q-TOP, motivated by Hoffmann (Arch Math 33:258–262, 1979) and Singh and Srivastava (Quaest. Math. 36: 167–179, 2013)