SAMS Subject Classification Number: 13

In this talk, I shall introduce \(J\)-frames, which is the pointfree counterpart of the concept of \(J\)-spaces which was exhibited by E. Michael in 2000. Some characterisations of \(J\)-frames via closed and relatively connected sublocales will be furnished. A common property between the remainder of any frame in a perfect compactification and the remainder of a \(J\)-frame in any compactification will be discussed and utilised to show that a completely regular frame is a \(J\)-frame if and only if its remainder is relatively connected in its Stone-Čech compactification. Among other things, I will show that a non-spatial frame is a \(J\)-frame if and only if it is connected.