# Tagged Questions

The study of vector space with a topology which makes the maps which sums two vectors and which multiply a vector by a scalar continuous. It's a natural generalization of normed spaces.

1answer
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### How strong is the operator norm topology?

Let $(V,\tau_V), (W,\tau_W)$ be normable topological vector spaces. Let $||\cdot||_V, ||\cdot||_W$ be norms on $V,W$ inducing $\tau_V, \tau_W$ respectively. Let $||\cdot||_{op}$ be the operator norm ...
0answers
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### Norms on $L(V,W)$

Let $V,W$ be normable topological vector spaces over $\mathbb{F}$. Let $C(V,W)$ be the set of continuous linear transformations $T:V\rightarrow W$. Let $||\cdot||_V, ||\cdot||_W$ be norms on $V,W$ ...
1answer
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### Does every Hamel basis for an infinite dimensional topological vector space have a maximal countable spanning subset?

‎‎‎‎Let ‎$X$ ‎be an infinite dimensional topological vector space and ‎$\{ e‎_{i}: i ‎\in I ‎\}$‎ be a Hamel basis for $X$. Does there exist a maximal countable subset ‎$J‎\subset ‎I$ ‎such ‎...
1answer
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