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=''):