γ-Frames, GΓ-Algebras and Measurable Spaces

The category of γ -Frm of γ-frames, which is isomorphic to the category GΓ-Alg of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb D$\end{document}-algebras satisfying certain identities, and the category γ -Top of γ-topological spaces provide the background for the category γ -Mbl of γ-measurable spaces. As in the category of frames, the functor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega_\gamma: \gamma {\text{ - }}Top \ni (X,\Omega_X) \mapsto \Omega_\S \in \gamma {\text{ - }}Frm^{op}$\end{document} has a right adjoint \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Pt_\gamma: G\Gamma {\text{ - }}Alg^{op} \to \gamma {\text{ - }}Top$\end{document}.