## Mathematical Subject Classification – MSC2010

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

Instructional exposition (textbooks, tutorial papers, etc.) 852

Research exposition (monographs, survey articles) 1266

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

Locally convex Fréchet spaces and (DF)-spaces 1374

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1028

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 606

Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $\Bbb R$, etc.) 695

Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 761

Topological invariants ((DN), ($\Omega$), etc.) 97

Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 239

Isomorphic theory (including renorming) of Banach spaces 1813

Compactness in Banach (or normed) spaces 285

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4401

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1588

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 90

Generalizations of inner products (semi-inner products, partial inner products, etc.) 307

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1133

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 967

Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 9667

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 449

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 7857

(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60 (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 552

Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20] 6187

Nonselfadjoint (sub)algebras in algebras with involution 70

Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 20349

Homological methods (exact sequences, right inverses, lifting, etc.) 222