Fixes issue #3826 and #4791:
Have SocketIO objects update their reference count in the underlying
socket object on close() so that the underlying socket object is
closed immediately when the last user is done rather than at an
unknown later time when garbage collection can do it.
diff --git a/Lib/socket.py b/Lib/socket.py
index 045987c..737930d 100644
--- a/Lib/socket.py
+++ b/Lib/socket.py
@@ -225,11 +225,12 @@
         return self._writing and not self.closed
 
     def fileno(self):
+        self._checkClosed()
         return self._sock.fileno()
 
     @property
     def name(self):
-        return self._sock.fileno()
+        return self.fileno()
 
     @property
     def mode(self):
@@ -239,9 +240,12 @@
         if self.closed:
             return
         io.RawIOBase.close(self)
+        self._sock._decref_socketios()
+        self._sock = None
 
     def __del__(self):
-        self._sock._decref_socketios()
+        if not self.closed:
+            self._sock._decref_socketios()
 
 
 def getfqdn(name=''):
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 51f41a9..b0fe057 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -856,6 +856,16 @@
         self.assertEqual(self.cli_file.mode, 'wb')
         self.assertEqual(self.cli_file.name, self.serv_conn.fileno())
 
+    def testRealClose(self):
+        self.serv_file.close()
+        self.assertRaises(ValueError, self.serv_file.fileno)
+        self.cli_conn.close()
+        self.assertRaises(socket.error, self.cli_conn.getsockname)
+
+    def _testRealClose(self):
+        pass
+
+
 class UnbufferedFileObjectClassTestCase(FileObjectClassTestCase):
 
     """Repeat the tests from FileObjectClassTestCase with bufsize==0.
@@ -881,6 +891,29 @@
         self.cli_file.write(b"B. " + MSG)
         self.cli_file.flush()
 
+    def testMakefileClose(self):
+        # The file returned by makefile should keep the socket open...
+        self.cli_conn.close()
+        msg = self.cli_conn.recv(1024)
+        self.assertEqual(msg, MSG)
+        # ...until the file is itself closed
+        self.serv_file.close()
+        self.assertRaises(socket.error, self.cli_conn.recv, 1024)
+
+    def _testMakefileClose(self):
+        self.cli_file.write(MSG)
+        self.cli_file.flush()
+
+    def testMakefileCloseSocketDestroy(self):
+        refcount_before = sys.getrefcount(self.cli_conn)
+        self.serv_file.close()
+        refcount_after = sys.getrefcount(self.cli_conn)
+        self.assertEqual(refcount_before - 1, refcount_after)
+
+    def _testMakefileCloseSocketDestroy(self):
+        pass
+
+
 class LineBufferedFileObjectClassTestCase(FileObjectClassTestCase):
 
     bufsize = 1 # Default-buffered for reading; line-buffered for writing
diff --git a/Misc/NEWS b/Misc/NEWS
index 42637dd..442cc1f 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -111,6 +111,10 @@
 Library
 -------
 
+- Issue #3826 and #4791: The socket module now closes the underlying socket
+  appropriately when it is being used via socket.makefile() objects
+  rather than delaying the close by waiting for garbage collection to do it.
+
 - Issue #3860: GzipFile and BZ2File now support the context manager protocol.
 
 - Issue #4867: Fixed a crash in ctypes when passing a string to a