Is table_open_cache a private cache of a session?

[Cui Shijun]

hi,
  I'm a little confused by the
document(http://dev.mysql.com/doc/refman/5.1/en/table-cache.html),
which only says:
"To minimize the problem with multiple client sessions having
different states on the same table, the table is opened independently
by each concurrent session."
  Are sessions using private table caches?
  if I have M concurrent sessions and N tables, assume each session
will access tables one by one, will mysql open M*N tables?