Definition talk:Topological Vector Space

The topology on $V$ is not inherited from $K$ - this only really makes sense in finite dimensions ie if $V = K^n$. When we say $\cdot : K \times V \to V$ should be continuous, we mean as a map from $\struct {K \times V, \tau_K \times \tau_V}$ (where $\tau_K \times \tau_V$ is the product topology of $\tau_K$ and $\tau_V$) to $\struct {V, \tau_V}$. So $\tau_V$ is dependent on $\tau_K$ somehow. I went through the verbosity on the other talk page. Caliburn (talk) 13:44, 18 February 2023 (UTC)


 * This complexity is currently swept under the rug, making it difficult to understand what is going on. Perhaps the fault is with me not having studied the right books. --prime mover (talk) 14:43, 18 February 2023 (UTC)