Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
74447
How do I divide a function into even and odd sections?
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
71442
How to prove $\det(I+uv^\intercal)=1+v^\intercal u$
70264
Prove that the inverse image of an open set is open
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
20467
Show that $(y_n)\in l^q$
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
98098
Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.
128917
Inner Product on $\mathbb{R}$ and on $\mathbb{C}$
9003
prove $\frac{1}{2}\mathbf{\nabla (u \cdot u) = u \times (\nabla \times u ) + (u \cdot \nabla)u}$ using index notation
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
99821
Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$