## Mathematics Subject Classification – MSC2010

General reference works (handbooks, dictionaries, bibliographies, etc.) 93

Instructional exposition (textbooks, tutorial papers, etc.) 967

Research exposition (monographs, survey articles) 1418

Explicit machine computation and programs (not the theory of computation or programming) 3

Locally convex Fréchet spaces and (DF)-spaces 1408

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1049

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 654

Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $\Bbb R$, etc.) 724

Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 791

Topological invariants ((DN), ($\Omega$), etc.) 107

Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 250

Isomorphic theory (including renorming) of Banach spaces 1984

Compactness in Banach (or normed) spaces 376

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4731

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1741

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 102

Generalizations of inner products (semi-inner products, partial inner products, etc.) 345

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1426

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1019

Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10597

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 504

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 8347

Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20] 6629

Nonselfadjoint (sub)algebras in algebras with involution 79

Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 22636

Homological methods (exact sequences, right inverses, lifting, etc.) 249