By all means buy a bed for your cat if you wish: but do not be surprised if it settles for its own choice of sleeping place. You have more chance of training a kitten than an adult to sleep where you want but that may largely be by restricting choice.
Most cats do not feel secure at floor level and they often prefer to be high up. Try a cushion somewhere high up that your cat has easy access to, preferably under an electric light fitting, so you can leave a 60 watt bulb burning as warmth for the cat when you have your main heating off.
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