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asyncore.file_wrapper duplicates file descriptor of given file and closes it in it's close method.
But unlike socket.socket class it does not automatically call close when object is garbage collected.
Users of regular sockets and asyncore.dispatcher do not experience resource leaks when they forget to call self.close() in handle_close().
But people using file_dispatcher do loose file descriptor every time file_wrapper object is garbage collected without calling self.close() first.

Adding a patch that adds an __exit__ function much like the one that socket.socket implements. Passes the test_asyncore & also doesn't raise a resource warning when I explicitly comment out some close() calls on file wrapper objects in the test.

Adding __exit__ will not make asyncore.file_wrapper close file descriptor when garbage collected.
Here is clone of socket.py solution for the same problem.
 def close(self):
 if self.fd:
 os.close(self.fd)
 self.fd = None # or maybe self.fd = 0 will be better
 def __del__(self):
 try:
 self.close()
 except:
 # close() may fail if __init__ didn't complete
 pass

New changeset ae12a926e680 by Victor Stinner in branch '3.4':
Issue #11453: asyncore: emit a ResourceWarning when an unclosed file_wrapper
http://hg.python.org/cpython/rev/ae12a926e680 

I fixed the issue in Python 3.4 and 3.5, thanks for the report.
In Python 3.4+, it's safe to add a destructor (__del__ method): even if the object is part of a reference cycle, it will be destroyed. It's not the case in Python 2.7. I prefer to leave Python 2.7 unchanged to limit the risk of regression.

New changeset 7c9335d97628 by Victor Stinner in branch 'default':
(Merge 3.4) Issue #11453: asyncore: emit a ResourceWarning when an unclosed
http://hg.python.org/cpython/rev/7c9335d97628 

New changeset 379aad232000 by Victor Stinner in branch '3.4':
Issue #11453, #18174: Fix leak of file descriptor in test_asyncore
http://hg.python.org/cpython/rev/379aad232000
New changeset 0ced2d2325fb by Victor Stinner in branch 'default':
(Merge 3.4) Issue #11453, #18174: Fix leak of file descriptor in test_asyncore
http://hg.python.org/cpython/rev/0ced2d2325fb