diff --git a/Doc/library/functions.rst b/Doc/library/functions.rst
--- a/Doc/library/functions.rst
+++ b/Doc/library/functions.rst
@@ -786,11 +786,14 @@
    expression.  If *x* is not a Python :class:`int` object, it has to define an
    :meth:`__index__` method that returns an integer.
 
+   .. index::
+      single: file object; open() built-in function
+
 
 .. function:: open(file, mode='r', buffering=-1, encoding=None, errors=None, newline=None, closefd=True, opener=None)
 
-   Open *file* and return a corresponding stream.  If the file cannot be opened,
-   an :exc:`OSError` is raised.
+   Open *file* and return a corresponding :term:`file object`.  If the file
+   cannot be opened, an :exc:`OSError` is raised.
 
    *file* is either a string or bytes object giving the pathname (absolute or
    relative to the current working directory) of the file to be opened or
@@ -910,7 +913,8 @@
       The *opener* parameter was added.
       The ``'x'`` mode was added.
 
-   The type of file object returned by the :func:`open` function depends on the
+   The type of :term:`file object` returned by the :func:`open` function
+   depends on the
    mode.  When :func:`open` is used to open a file in a text mode (``'w'``,
    ``'r'``, ``'wt'``, ``'rt'``, etc.), it returns a subclass of
    :class:`io.TextIOBase` (specifically :class:`io.TextIOWrapper`).  When used
diff --git a/Doc/library/io.rst b/Doc/library/io.rst
--- a/Doc/library/io.rst
+++ b/Doc/library/io.rst
@@ -16,11 +16,15 @@
 Overview
 --------
 
-The :mod:`io` module provides Python's main facilities for dealing for various
-types of I/O.  There are three main types of I/O: *text I/O*, *binary I/O*, *raw
-I/O*.  These are generic categories, and various backing stores can be used for
-each of them.  Concrete objects belonging to any of these categories will often
-be called *streams*; another common term is *file-like objects*.
+.. index::
+   single: file object; io module
+
+The :mod:`io` module provides Python's main facilities for dealing with various
+types of I/O.  There are three main types of I/O: *text I/O*, *binary I/O*
+and *raw I/O*.  These are generic categories, and various backing stores can
+be used for each of them.  A concrete object belonging to any of these
+categories is called a :term:`file object`.  Other common terms are *stream*
+and *file-like object*.
 
 Independently of its category, each concrete stream object will also have
 various capabilities: it can be read-only, write-only, or read-write. It can