If $x_1\ne x_2$ then there exists $y$ in dual space such that $y(x_1)\ne y(x_2)$
104607
Hahn-Banach theorem, dual space
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
113002
Any power of $(X_1, X_2,...,X_i)$ is primary in $k[X_1, X_2,...,X_n].$
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
15354
Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
48557
Product of connected spaces
101486
Understanding that $A = \{x\in \ell_2: |x_n| \leq \frac{1}{n}, n = 1,2,...\}$ is compact in $l_2$.
49087
Show that a norm on an inner product space satisfies parallelogram law.
90525
The subspace of $\ell_2$
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
85819
A non-polyhedral pair $(X,A)$ with both $X$ and $A$ polyhedral
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
18839
Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$