ridges 6 rested on the top edge of the flanges 10 on the retainer 7 as shown in fig8 not only is the gripper 1 kept from falling off the retainer 7 but also its grip plates 3 are prevented from spreading out by being elastically pushed by the mop 8 thus the mop 8 is firmly held by the gripper 1 received in the retainer 7 as shown in fig9 the retainer 7 presses upon the grip plates 3 over substantially their whole length and the mop stoppers 5 adapted to bite into the mop 8 are provided on the inner surfaces of the grip plates 3 over substantially the whole length so that the top portion of the mop 8 is held firmly with a uniform force over its entire length to dismount the mop 8 the gripper 1 is pulled out of the retainer 7 and its grip plates 3 are spread open to draw the mop stoppers 5 out of the mop 8 the mop stoppers 5 may be in the form of serrations projections ridges or combinations thereof the retainer 7 should preferably have its side plates 9 coupled together at one end thereof by means of a coupling member 11 and the gripper 1 should be provided with another coupling member 12 at one end thereof in such a manner.