A safety closure (100, 200, 300, 433, 600, 700) comprising: an adaptor (102, 202, 302, 457, 702) defining an axial bore (110, 210, 310) and an outer radial surface, the outer radial surface defining a first plurality of radial ridges arranged in discrete groupings and a plurality of gaps extending in an axial direction between groupings of the first radial ridges; a cap (104, 204, 304, 459, 604, 704) including a top wall (138, 346), a sidewall (148, 348), and a bottom (150, 350), the sidewall (148, 348) having an outer radial surface and an inner radial surface, the inner radial surface defining a receiving space (152, 752), the cap having a second plurality of radial ridges arranged in discrete groupings on the inner radial surface, the receiving space being arranged to receive an upper portion of the adaptor (102, 202, 302, 457, 702) and the second radial ridges being arranged to selectively mate with and engage the first plurality of radial ridges of the adaptor to secure the cap on the adaptor, the bottom (150, 350) having a locking channel, slot, or notch (156, 756); and a locking system (106, 606, 706) attached to the cap (104, 204, 304, 459, 604, 704) and including a locking arm (174, 774) attached to the cap (104, 204, 304, 459, 604, 704) with a lock piece (190, 790) arranged to selectively protrude through the locking channel, slot, or notch (156, 756) in the bottom (150, 350) of the cap (104, 204, 304, 459, 604, 704) and into the receiving space (152, 752) of the cap to lock the first plurality of radial ridges in engagement with the second plurality of radial ridges, characterized in that the lock piece (190, 790) is configured to engage a second end of at least one of the first plurality of radial ridges to prevent the cap (104, 204, 304, 459, 604, 704) from moving from an engaged position to a disengaged position. an adaptor (102, 202, 302, 457, 702) defining an axial bore (110, 210, 310) and an outer radial surface, the outer radial surface defining a first plurality of radial ridges arranged in discrete groupings and a plurality of gaps extending in an axial direction between groupings of the first radial ridges; a cap (104, 204, 304, 459, 604, 704) including a top wall (138, 346), a sidewall (148, 348), and a bottom (150, 350), the sidewall (148, 348) having an outer radial surface and an inner radial surface, the inner radial surface defining a receiving space (152, 752), the cap having a second plurality of radial ridges arranged in discrete groupings on the inner radial surface, the receiving space being arranged to receive an upper portion of the adaptor (102, 202, 302, 457, 702) and the second radial ridges being arranged to selectively mate with and engage the first plurality of radial ridges of the adaptor to secure the cap on the adaptor, the bottom (150, 350) having a locking channel, slot, or notch (156, 756); and a locking system (106, 606, 706) attached to the cap (104, 204, 304, 459, 604, 704) and including a locking arm (174, 774) attached to the cap (104, 204, 304, 459, 604, 704) with a lock piece (190, 790) arranged to selectively protrude through the locking channel, slot, or notch (156, 756) in the bottom (150, 350) of the cap (104, 204, 304, 459, 604, 704) and into the receiving space (152, 752) of the cap to lock the first plurality of radial ridges in engagement with the second plurality of radial ridges, characterized in that the lock piece (190, 790) is configured to engage a second end of at least one of the first plurality of radial ridges to prevent the cap (104, 204, 304, 459, 604, 704) from moving from an engaged position to a disengaged position.