How to prove if $\bigcup_{k=1}^{n}V_{k}$ is a subspace over $\mathbb{C}$ then $\bigcup_{k=1}^{n}V_{k}=V_{j}$ for some j?
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
138653
Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
27629
How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
41013
Subspace of $C^3$ that spanned by a set over C and over R
70413
A vector space over $R$ is not a countable union of proper subspaces
95321
Subspaces of all real-valued continuous functions on $\mathbb{R}^1$
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
67191
When is the union of a family of subspaces of a vector space also a subspace?
70543
Does an uncountable discrete subspace of the reals exist?
139988
Counter example for a result of intersection of subspaces