# Tagged Questions

31 views

### Linear bijection non-preserving Hausdorff propery

My question is: If $f: X \to Y$ is a continuous and linear bijection between topological vector spaces, is it possible that $X$ is Hausdorff and $Y$ is non-Hausdorff? (TVSs are considered in the more ...
52 views

### Example for finite dimensional analog of integral transforms

I understand that integral transforms are generalisations of the dot product of functions that could be interpreted as infinite dimensional vectors. The most significant advantage then is that ...
103 views

### Linear algebra. Find a counter-example

this is the statement: if $\vec v_{1}, \vec v_{2} , \vec v_{3}, \vec v_{4}$ is a basis for the vector space $\Bbb R^{4}$, and W is a subspace of $\Bbb R^{4}$, then some subset of the $\vec v$ 's is a ...
121 views

### A finite dimensional vector space that is not naturally isomorphic to its dual.

I need an example of a finite dimensional vector space $V$ that is not naturally isomorphic to $V^\ast$. I know that, at least in finite dimensional case, there is a one-to-one correspondence between ...
315 views

### Other guises for the vector space $\mathbb{R}^n$?

One way the vector space $\mathbb{R}^n$ can come up is as the space of polynomials over $\mathbb{R}$ of degree at most $(n-1)$ . Here we have the isomorphism: (a_0,a_1,\ldots,a_{n-1}) ...
1k views

433 views

### Example for a proper dense subspace?

I have been reading some books on functional analysis, and many of them keep talking about a vector space along with a dense proper subspace of it (especially when constructing counterexamples). But ...