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Currently the prototype uses timeout=socket._GLOBAL_DEFAULT_TIMEOUT, and the docs give the prototype as:
 urlopen(url, data=None[, timeout], *, cafile=None, capath=None)
which is unlike most other Python function prototypes in the docs, and makes no sense from a python syntax point of view. The current implementation makes it impossible to explicitly request the default timeout unless you look in the code and use the marked-private attribute of the socket module.
I suggest the prototype be changed to either timeout=None with an explanation that that means "use the default socket timeout", or to some public sentinel that can be passed explicitly. I believe there are a number of other examples in the stdlib of None meaning "use the default", so I favor the former.

Quick little patch to change the default to None and update the corresponding documentation.

Thanks. Looks good to me. I'll give Senthil a little time to comment, in case he disagrees with my proposal, before committing it.
We could conceivably apply this as a bug fix to 3.2, since I don't think there is any backward compatibility issue.

I think the same change is needed in function open(url, data=None[, timeout]) of OpenerDirector. I added this other patch.

Well, it turns out that this design is intentional, because actually using the global socket timeout is deprecated (see issue 2451). (That is, the non-None default value of the timeout parameter is a backward compatibility hack.)
So I'm closing this as invalid. Sorry for the confusion, and thanks for the patches, even though they didn't get used this time. (They did help me realize the issue was invalid though, because the tests didn't pass when I applied them!)
I still don't like the doc artifact, but I can't think of a way to improve it given the nature of the API.

Hi David,
I am sorry, I did not notice your second comment in this bug and later when you closed this, noticed the bug report. 
Yes, the default=None but actually pointing to a sentinel value is an odd duck and I believe the explanation in docs were updated a couple of times to inform user of that behavior, but still the signature gives a feeling that it could be improved. I am at loss as well in terms of giving an "easy solution" to fix the docs.
Thanks,
Senthil