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Feb 12, 2011 at 16:30 comment added Amit Kumar Gupta Why would the existence of the product require choice? The non-emptiness of the product requires choice, but if it's empty, it's regular anyways.
Feb 12, 2011 at 16:20 comment added Peter Krautzberger Francois, just tiny addition: the existence of the product space does of course require AC. I know it's silly to mention, but maybe that was the OP's real issue, 'uncountable product' an all...
Feb 12, 2011 at 11:51 history answered François G. Dorais CC BY-SA 2.5