I would like to trow away some confusion I'm accumulating.
- Usually when superstrings are introducted (see for example Wikipedia) one says: Type I is a theory of open and closed strings, while Type II (A and B) is a theory of only closed strings. That is ok;
- After some exploration ones find that one of most important object in Type II theory are Dbrane, where, by definition, open strings can end. So in Type II theory there are open string. As you can see at page 53 of the PDF, Tong affirm:
For type II superstrings, the open strings and Dbranes are necessary ingredients.
How can the apparent tension (if not contraddiction) of points 1. 2. be solved?