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Mathematical Sciences Classification System

46Axx - Topological linear spaces and related structures
{For function spaces, see 46Exx}

• 13
  46A03
  General theory of locally convex spaces
• 46A04
  Locally convex Fréchet spaces and (DF)-spaces
• 46A08
  Barrelled spaces, bornological spaces
• 2
  46A11
  Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
• 2
  46A13
  Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
• 4
  46A16
  Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
• 2
  46A17
  Bornologies and related structures; Mackey convergence, etc.
• 1
  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
• 2
  46A22
  Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
• 46A25
  Reflexivity and semi-reflexivity [See also 46B10]
• 1
  46A30
  Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
• 2
  46A32
  Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
• 3
  46A35
  Summability and bases [See also 46B15]
• 13
  46A40
  Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
• 5
  46A45
  Sequence spaces (including Köthe sequence spaces) [See also 46B45]
• 1
  46A50
  Compactness in topological linear spaces; angelic spaces, etc.
• 5
  46A55
  Convex sets in topological linear spaces; Choquet theory [See also 52A07]
• 46A61
  Graded Fréchet spaces and tame operators
• 46A63
  Topological invariants ((DN), ($\Omega$), etc.)
• 46A70
  Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
• 2
  46A80
  Modular spaces
• 1
  46A99
  None of the above, but in this section