## Mathematics Subject Classification – MSC2010

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

Instructional exposition (textbooks, tutorial papers, etc.) 976

Research exposition (monographs, survey articles) 1435

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

Locally convex Fréchet spaces and (DF)-spaces 1412

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.) 660

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) 794

Topological invariants ((DN), ($\Omega$), etc.) 108

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

Isomorphic theory (including renorming) of Banach spaces 2005

Compactness in Banach (or normed) spaces 384

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4767

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1762

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 106

Generalizations of inner products (semi-inner products, partial inner products, etc.) 349

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1445

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1024

Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10671

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 505

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 8390

Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20] 6673

Nonselfadjoint (sub)algebras in algebras with involution 80

Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 22893

Homological methods (exact sequences, right inverses, lifting, etc.) 252