Apparatus for securing a first object to a second object, the apparatus comprising: an elongated body having a distal end, a proximal end, and a lumen extending between the distal end and the proximal end, the lumen comprising a first section and a second section, the first section of the lumen being disposed distal to the second section of the lumen, and with the first section of the lumen having a wider inner diameter than the second section of the lumen; wherein the elongated body comprises at least one longitudinally-extending slit extending through the side wall of the elongated body and communicating with the lumen, the proximal end of the at least one longitudinally-extending slit being spaced from the proximal end of the elongated body; an elongated element extending through the lumen of the elongated body, the elongated element comprising a proximal end and a distal end, the elongated element having an enlargement at its distal end, the enlargement having an outer diameter greater than the inner diameter of the second section of the lumen and having an outer diameter smaller than the inner diameter of the first section, and wherein the elongated element is constructed such that proximal movement of the elongated element causes proximal movement of the enlargement into the second section of the lumen, whereby to radially expand the elongated body without splitting the distal end of the elongated body, and wherein the distal end of the at least one longitudinally-extending slit is spaced from the distal end of the elongated body and wherein the second section of the lumen of the elongated body, when not expanded by the enlargement, has a constant inner diameter. an elongated body having a distal end, a proximal end, and a lumen extending between the distal end and the proximal end, the lumen comprising a first section and a second section, the first section of the lumen being disposed distal to the second section of the lumen, and with the first section of the lumen having a wider inner diameter than the second section of the lumen; wherein the elongated body comprises at least one longitudinally-extending slit extending through the side wall of the elongated body and communicating with the lumen, the proximal end of the at least one longitudinally-extending slit being spaced from the proximal end of the elongated body; an elongated element extending through the lumen of the elongated body, the elongated element comprising a proximal end and a distal end, the elongated element having an enlargement at its distal end, the enlargement having an outer diameter greater than the inner diameter of the second section of the lumen and having an outer diameter smaller than the inner diameter of the first section, and wherein the elongated element is constructed such that proximal movement of the elongated element causes proximal movement of the enlargement into the second section of the lumen, whereby to radially expand the elongated body without splitting the distal end of the elongated body, and wherein the distal end of the at least one longitudinally-extending slit is spaced from the distal end of the elongated body and wherein the second section of the lumen of the elongated body, when not expanded by the enlargement, has a constant inner diameter.