Abstract:A locallic version of Hager's metric-fine spaces is presented. A general definition of $\Cal A$-fineness is given and various special cases are considered, notably $\Cal A =$ all metric frames, $\Cal A =$ complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.
Keywords: uniform frames and sigma frames, fine, metric-fine, completion
AMS Subject Classification: 54A05, 54D20, 54E15, 06B99, 54D30, 54E35, 06A23