A solution is proposed for closing a mouth (125) of a container (110) of a liquid (105). A corresponding closure (135) comprises a cap (205) having fixing means (318) for fixing the cap (205) to the container (110), the cap (205) being rotatable around a longitudinal axis (203) of the container (110) in a fixed condition wherein the closure (135) is fixed to the container (110), a delivery port (336) for delivering the liquid (105) from the container (110), a cap suction conduit (345) for suctioning air into the container (110) during the delivering of the liquid (105) and a connector (342) for connecting a delivery device (805) of the liquid (105), the connector (342) being in fluid communication with the delivery port (336), a cursor (210) having a thread (406) for screwing the cursor (205) with respect to the container (110), a valve member (424) in a closed position wherein the valve member (215) closes the delivery port (336), and a cursor suction conduit (433) slidebly coupled with the cap suction conduit (345), a frangible element (351) closing the cap suction conduit (345) or the cursor suction conduit (433), and dragging means (327, 409) for dragging the cursor (210) into rotation by the cap (205), wherein the closure (135) is configured to cause the cursor (210) to slide with respect to the cap (205) in response to at least one rotation of the cap (205) thereby moving the cursor suction conduit (433) to break the frangible element (351), putting in fluid communication the cursor suction conduit (433) with the cap suction conduit (345), and moving the valve member (424) to an open position, wherein the valve member (215) opens the delivery port (336).