If $M$ be a submanifold of $N$, is true that $TM$ is a submanifold of $TN$?
68197
If $F:M\to N$ is a smooth embedding, then so is $dF:TM\to TN$.
42913
Equivalence of the definition of the Subbasis of a Topology
132063
locally on $S$ one of the coordinates is a $C^∞$ function of the other coordinate. Show that $S$ is a submanifold of $R^2$
61255
Tangent bundle : is a manifold
132653
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
73172
Is every complex (smooth) manifold a scheme?
75614
Proving that $n|m\implies f_n|f_m$
122410
Can one build a homology theory using submanifolds and their boundaries?
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
76937
Is there an elementary way to see that there is only one complex manifold structure on $R^2$?
40256
Why are these two descriptions of real n-dimensional projective space  the same?
10998
Embedding $S_n$ in $A_{2n}$
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
4295
Let $N$, $K$ be sub-modules of $M$ with $I=\mathrm{Ann}(N)$, $J=\mathrm{Ann}(K)$. Show $I+J$ is a proper subset of $\mathrm{Ann}(N \cap K)$.
79711
How to show $\omega^n$ is a volume form in a symplectic manifold $(M, \omega)$?
43136
Branch of the n-th root of a holomorphic function is holomorphic