The dual vector space is always complete.
98759
Proof of "Dual normed vector space is complete"
124786
Prove that V contains a subspace of each dimension
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
152325
Every subspace of the dual of a finite-dimensional vector space is an annihilator
76110
Proving that the zero vector is unique
52865
Topological Vector Space: $\dim Z\text{ finite}\implies Z\text{ closed}$
125610
Space of bounded continuous functions is complete
59446
Universal property of universal bundles.
121732
Functional completeness of $\{\text{or},\text{ xor}, \text{ xnor}\}$
91173
Finite-dimensional subspace normed vector space is closed
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
81379
Any two bases of a finite dimensional vector space must have the same number of elements.
28238
A question about long exact sequence of finite dim vector spaces
53850
Proof that every normed vector space is a topological vector space
115999
Is there always an injective map from a space in its dual space?
124042
Why is a vector space equal to its tangent space for any point?
132300
Dimensions of vector spaces in an exact sequence