## Mathematics Subject Classification – MSC2010

General reference works (handbooks, dictionaries, bibliographies, etc.) 94

Instructional exposition (textbooks, tutorial papers, etc.) 992

Research exposition (monographs, survey articles) 1483

Explicit machine computation and programs (not the theory of computation or programming) 4

Locally convex Fréchet spaces and (DF)-spaces 1429

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1053

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 672

Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb R\), etc.) 731

Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness) 798

Topological invariants ((DN), (\(\Omega\)), etc.) 111

Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 255

Isomorphic theory (including renorming) of Banach spaces 2037

Compactness in Banach (or normed) spaces 409

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4875

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1817

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 109

Generalizations of inner products (semi-inner products, partial inner products, etc.) 361

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1522

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1041

Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10951

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 519

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 8534

(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60 (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 706

Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20] 6852

Nonselfadjoint (sub)algebras in algebras with involution 81

Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) [See also 22D25, 47Lxx] 23563

Homological methods (exact sequences, right inverses, lifting, etc.) 261