Let $V$ be a vector space and $U,W$ be its subspaces. Prove that if the union $U\cup W$ is a subspace of $V$, then $W \subseteq U$ or $U \subseteq W$
11301
Union of two vector subspaces not a subspace?
22295
Subspace of a separable space is separable
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
102924
Normal space- equivalent condition: $\forall U, V$ - open $: U \cup V = X \ \ \ \exists F \subset U \ , G \subset V$ - closed $: F \cup G = X$
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?
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
85239
Proof $dim(W)=dim(V)=n \implies W=V$
4151
Every subspace of a vector space has a complement
95513
Proving $W$ is a subspace of $P_{2}$
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $