A visiting friend

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I have a doggy that visits me almost everyday. I tried to not let the dog get to attached to me, or more so, let me get attached to the dog. :) The problem is I have and the dog has recently started to sometimes even sleep in front of my door. The Question : Is it appropriate for me to ask the owner if I can keep him?, if I can find the owner. Or do I distance myself from the dog altogether?