\(E\)-compactness in pointfree topology (Q1395750)

The author presents a pointfree analogue of \(E\)-compactness as introduced by Engelking and Mrowka. Main results: 1. Let \(E\) be a regular frame, and \(L\) an \(E\)-regular frame. Then the following are equivalent: (1) \(L\) is \(E\)-complete. (2) \(L\) is a closed quotient of a copower of \(E\). (3) Every \(C_E\)-extension of \(L\) is an isomorphism. 2. The category of all \(E\)-compact frames is coreflective in the category of all \(E\)-regular frames. 3. The spatial \(E\)-compact frames are precisely those frames that are spatial reflections of \(E\)-complete frames. 4. The category of \(E\)-compact frames is closed under coproducts and closed quotients.