Can we always say, for finite-dimensional spaces, that there is no canonical isomorphism between $V$ and $V^*$?
74675
Why is there no natural isomorphism between $V$ and its dual?
151425
Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
90071
Why don't we have an isomorphism between $R[x]$ and $ R[[x]]$?
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
115999
Is there always an injective map from a space in its dual space?
125982
If the dual spaces are isometrically isomorphic are the spaces isomorphic?
99382
What is needed to make Euclidean spaces isomorphic as groups?
81238
Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
143517
Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
76572
What facts about the weak topology fail in spaces that aren't Banach?
107389
Show that the vector space of real functions is not finitely spanned
42362
Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals
139176
The real line is not homeomorphic to any non-trivial product space
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
78654
An example of a norm which can't be generated by an inner product
6101
Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?