## 46Axx

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### Topological linear spaces and related structures

{For function spaces, see 46Exx}
46A03 General theory of locally convex spaces
46A04 Locally convex Fréchet spaces and (DF)-spaces
46A08 Barrelled spaces, bornological spaces
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A17 Bornologies and related structures; Mackey convergence, etc.
46A19 Other topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
46A20 Duality theory
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
46A63 Topological invariants ((DN), ($\Omega$), etc.)