In reply to danielmoss:
The rope cutter in the shop and at the manufacturer is a "hot knife". It's a piece of wire heated up by electrical resistance until it melts the nylon on contact, cutting the rope and melting core and sheath together. At home you can use a literal hot knife - a cheap kitchen knife heated in a gas flame (it ruins the temper of the steel, so don't use your favourite chef's knife).
In any case, a separation of core and sheath for 5mm at the end doesn't matter one jot in terms of the actual strength of the rope, especially as there will nearly always be a knot in the rope between the end and the bit being weighted. The core and sheath aren't magically attached together along the length of the rope either, and they can move relatively over time - it's known as sheath slippage, it's not particularly unsafe but it's unsightly and can make a rope hard to coil.