  We discuss a variant of the category of dendroidal sets, the so-called closed
dendroidal sets which are indexed by trees without leaves. This category
carries a Quillen model structure which behaves better than the one on general
dendroidal sets, mainly because it satisfies the pushout-product property,
hence induces a symmetric monoidal structure on its homotopy category. We also
study complete Segal style model structures on closed dendroidal spaces, and
various Quillen adjunctions to model categories on (all) dendroidal sets or
spaces. As a consequence, we deduce a Quillen equivalence from closed
dendroidal sets to the category of unital simplicial operads, as well as to
that of simplicial operads which are unital up-to-homotopy. The proofs exhibit
several new combinatorial features of categories of closed trees.
