===== Locally convex topological vector space =====
==== Set ====
>a vector space together with a family of seminorms

=== Discussion ===
This induces a norm.

Makes the
[[https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative | Gateaux derivative]]
possible, which is possibly non-linear and more general than the [[Frechet derivative]]

=== Reference ===
Wikipedia: 
[[https://en.wikipedia.org/wiki/Locally_convex_topological_vector_space|Locally convext topological v
ector space]]
[[https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative | Gateaux derivative]]

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=== Subset of ===
[[Vector space]]
=== requirements ===
[[Seminorm]]