## Mathematics Subject Classification – MSC2010

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

Instructional exposition (textbooks, tutorial papers, etc.) 970

Research exposition (monographs, survey articles) 1427

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

Locally convex Fréchet spaces and (DF)-spaces 1409

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1048

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 655

Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $\Bbb R$, etc.) 723

Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 792

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 1996

Compactness in Banach (or normed) spaces 380

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4748

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1755

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 103

Generalizations of inner products (semi-inner products, partial inner products, etc.) 346

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1433

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1022

Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10628

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 507

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 8369

Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20] 6650

Nonselfadjoint (sub)algebras in algebras with involution 80

Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 22750

Homological methods (exact sequences, right inverses, lifting, etc.) 251