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>>> f = io.StringIO()
>>> f.close()
>>> f.readable()
True
>>> f.read()
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
ValueError: I/O operation on closed file.
>>> f = io.BytesIO()
>>> f.close()
>>> f.readable()
True
>>> f.read()
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
ValueError: I/O operation on closed file

This also happens for the writable() and seekable() methods. The problem is that those methods do not check whether the buffers have been closed in stringio.c. This is fixed in the attached patch for StringIO. BytesIO should be the same, but bytesio.c is structured differently, and I still have to understand the code. I will try to do this, and then add tests for this issue - which should go in one of the mixins of test_memoryio.py, I presume.

Here is the patch fixing the issue in both StringIO and BytesIO. In both cases, the problem is that in their respective c files, these methods always returned true, without testing whether the file was closed. Is this a recent rewrite? I am surprised this did not bite someone earlier.
I also added a testcase to test_memoryio.py covering this issue; and I added the docstring for these methods, which were missing.
This patch compiles and passes the entire test suite in my system.

Ah, there's a misunderstanding. The methods should raise ValueError when the object has been closed.
See issue15840 for reference.

Sorry, I should have seen the related issue (or just read the docs :)).
Here is the patch fixing these issues, implementing the behaviour stated in the docs (raising ValueError after close). The tests revealed that the _pyio module also needed fixing, and this is done in the patch as well.

A couple of nits about the docstrings:
+PyDoc_STRVAR(stringio_seekable_doc,
+"seekable() -> Bool. Returns True if IO object can be seeked.");
First, "bool" should be lowercase. Also, in seekable(), "IO object" should be "the IO object".
Otherwise, looks fine to me.

Thanks. Here is the amended patch with your suggestions implemented.

Alessandro, have you already signed a contributor agreement so that your patch can be integrated?
If not, you'll find the instructions at http://www.python.org/psf/contrib/
Thank you!

I just emailed my contributor's agreement.

New changeset 524931e5aebf by Antoine Pitrou in branch '3.2':
Issue #15841: The readable(), writable() and seekable() methods of BytesIO
http://hg.python.org/cpython/rev/524931e5aebf
New changeset fcf097cb5f6b by Antoine Pitrou in branch 'default':
Issue #15841: The readable(), writable() and seekable() methods of BytesIO
http://hg.python.org/cpython/rev/fcf097cb5f6b
New changeset d0ab34d4c733 by Antoine Pitrou in branch '2.7':
Issue #15841: The readable(), writable() and seekable() methods of io.BytesIO
http://hg.python.org/cpython/rev/d0ab34d4c733 

I have now committed the patch. Thank you again!