In James.E.Munkres there is a theorem that says A finite cartesian product of connected space is connected. But what about infinite product spaces? Though there are few more question like this in the site some of them consider path connected or many other theorems that I don't understand. So if you can give a simple example that will be great. Thanks.
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Oh. OK. Thanks. – user426700 May 30 '17 at 11:17
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https://math.stackexchange.com/q/257981/4280 has a proof sketch (with some details filled in in its answer) of the arbitrary product case. – Henno Brandsma May 30 '17 at 13:22