# Is $TN$ a smooth embedded submanifold with or without boundary in $TM$?

Let $$M$$ be a smooth manifold with or without boundary, and $$N$$ a smooth embedded submanifold with or without boundary in $$M$$, then the inclusion map $$N\to M$$ induces $$TN\to TM$$, is $$TN$$ a smooth embedded submanifold with or without boundary in $$TM$$?

• Yes indeed. Just think of what the charts are. – user587399 Jul 18 at 14:47