The term surface used without qualification refers to surfaces without boundary. In particular, a surface with empty boundary is a surface in the usual sense. A surface with empty boundary which is compact is known as a 'closed' surface. The two-dimensional sphere, the two-dimensional torus, and the real projective plane are examples of closed surfaces.
The term surface used without qualification refers to surfaces without boundary In particular a surface with empty boundary is a surface in the usual sense A surface with empty boundary which is compact is known as a 'closed' surface The two-dimensional sphere the two-dimensional torus and the real projective plane are examples of closed surfaces