A rope termination (100; 200; 300; 400; 500) in a hollow-braided rope (110; 210; 310; 410; 510), said rope termination comprising: (a) a double-braided portion of the termination length L db of the hollow-braided rope (110; 210; 310; 410; 510) including an outer braid portion concentric with and surrounding an inner braid portion, the inner braid portion terminating in a tail; (b) a rope inverter (120; 220; 320; 420; 520) including a rope inverter body having a tapered rope inverter body outer surface , a rope inverter body inner surface defining a rope receiving channel through the rope inverter body, and a rope inversion surface connecting the rope inverter body outer surface and the rope inverter body inner surface , wherein the rope inverter (120; 220; 320; 420; 520) is configured such that: (i) a portion of the outer braid portion of the double-braided portion of the hollow-braided rope (110; 210; 310; 410; 510) wraps around at least part of the rope inverter body outer surface , (ii) a portion of the inner braid portion of the double-braided portion of the hollow-braided rope (110; 210; 310; 410; 510) is disposed within the rope receiving channel through the rope inverter body (120; 220; 320; 420; 520), and (iii) a portion of the double-braided portion of the hollow-braided rope wraps around at least part of the rope inversion surface of the rope inverter body (120; 220; 320; 420; 520); and (c) a socket including a socket body having a tapered socket body inner surface , the socket body inner surface defining a tapered bore through the socket body that forms a rope inverter receiving cavity configured to receive the rope inverter (120; 220; 320; 420; 520). (a) a double-braided portion of the termination length L db of the hollow-braided rope (110; 210; 310; 410; 510) including an outer braid portion concentric with and surrounding an inner braid portion, the inner braid portion terminating in a tail; (b) a rope inverter (120; 220; 320; 420; 520) including a rope inverter body having a tapered rope inverter body outer surface , a rope inverter body inner surface defining a rope receiving channel through the rope inverter body, and a rope inversion surface connecting the rope inverter body outer surface and the rope inverter body inner surface , wherein the rope inverter (120; 220; 320; 420; 520) is configured such that: (i) a portion of the outer braid portion of the double-braided portion of the hollow-braided rope (110; 210; 310; 410; 510) wraps around at least part of the rope inverter body outer surface , (ii) a portion of the inner braid portion of the double-braided portion of the hollow-braided rope (110; 210; 310; 410; 510) is disposed within the rope receiving channel through the rope inverter body (120; 220; 320; 420; 520), and (iii) a portion of the double-braided portion of the hollow-braided rope wraps around at least part of the rope inversion surface of the rope inverter body (120; 220; 320; 420; 520); and (c) a socket including a socket body having a tapered socket body inner surface , the socket body inner surface defining a tapered bore through the socket body that forms a rope inverter receiving cavity configured to receive the rope inverter (120; 220; 320; 420; 520). <EOS>