Assembly: Microsoft.SharePoint.Taxonomy (in Microsoft.SharePoint.Taxonomy.dll)
A TermSet is open if new Term objects can be added to it. It is closed if new terms cannot be added to it.
If the user is the term store administrator, group manager, or a term set owner, users can always use the term store manager page to add new Term objects to a TermSet object regardless of whether the TermSet is open or closed.
If the TermSet is open, use the Add new term link in the Term picker dialog box in the Web tagging user interface to add new Term objects.