Prove that if Y is a closed subspace of a normed linear space X and x \nin Y, the span of x and Y is closed.
43431
Show that $F+G$ is closed when $G$ a closed subspace of normed space $E$ and $F$ a finite dimensional subspace of $E$.
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
125073
Finite-dimensional subspaces of normed vector spaces are direct summands
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
3820
Prove that $||x|-|y||\le |x-y|$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
14840
$c_0$ is a closed subspace of $l^{\infty}$
120766
Prove ${y_n}$ is a basis for a Hilbert space $H$.
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
154762
Dual space of a finite dimensional normed space
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
57609
Hahn-Banach proof by extension of basis
41013
Subspace of $C^3$ that spanned by a set over C and over R
53261
Show that Pn is an (n+1)-dimensional subspace
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
141762
The direct sum of two closed subspace is closed? (Hilbert space)