Let A and B be subsets of the poset (P,\(\leq)\). A is said to be well below B, \(A\ll B\), if whenever D is a directed subset of P for which sup(D) exists and belongs to the upset \(\uparrow B\), one has that \(D\cap \uparrow A\neq \emptyset\). According to Gierz and Lawson, a lattice L is generalized continuous (a GCL), if one has for every x in L that \(\uparrow \{x\}=\cup \{\uparrow A| A\) finite and \(A\ll \{x\}\}\). The relation \(\rho\) between subsets A and B is defined like \(\ll\), but it is stronger: The condition must hold for any subset S, not only for directed sets D. The author now defines a lattice as generalized completely distributive (a GCD), if one has for any x in L that \(\uparrow \{x\}=\cup \{\uparrow A| A\) finite and \(A\rho\{\) \(x\}\}\). Because completely distributive lattices are GCD's (according to Raney), the GCD's generalize continuous lattices and completely distributive lattices at the same time. The author presents interesting algebraic and topological instances of this generalization.