Show that $U\cup W$ is a subspace of $V$ if and only if $U \subset W$ or $W \subset U$
11301
Union of two vector subspaces not a subspace?
53261
Show that Pn is an (n+1)-dimensional subspace
15576
Addition of two subspaces
65494
Proper subspaces of $ R^n $
4151
Every subspace of a vector space has a complement
41047
Subspace Topology of a subset
41520
Prove that $L(V,W)$ forms a vector space
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
147793
A variation on the induced topology (subspace topology)
29849
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
90525
The subspace of $\ell_2$
92774
Prove that a linear subspace of $C([0,1])$ is closed
6955
A Banach space is reflexive if and only if its dual is reflexive
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
150796
Subspace topology and order topology (2)
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then