The pia and arachnoid membranes are called leptomeninges (Orlando Regional Healthcare, 2004).
The delicate, spiderweb-like arachnoid layer, attached to the inside of the dura, surrounds the brain and spinal cord but does not line the brain down into its sulci (folds). Cerebrospinal fluid flows under this membrane in the subarachnoid space, which is full of the delicate fibres of the arachnoid extending down to attach to the pia mater.
The portions covering the brain and spinal cord are called arachnoidea encephali and arachnoidea spinalis, respectively.