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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 $TM$?

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

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