# How is algebraic topology used in linguistics

Regensburg composite classification

 SK 130 Logic and basics, metamathematics, Rem .: Nonstandard analysis (including the basics of analysis), structure of the number system, model theory, predicate calculus, proof theory, undecidability, two-valued and multi-valued logic, formal languages, semantics and linguistics, Boolean algebras, abstract automata Reg .: Abstract Automat || Analysis || Structure (Music Group) || Proof Theory || Boolean Algebra || Formal Language || Linguistics || Logical Language || Mathematical Logic || Multi-Value Logic || Metamathematics || Model Theory || Nonstandard- Analysis || predicate calculus || semantics || undecidability || number system
 SK 150 - SK 160 Set theory and association theory Rem .: ordered structures, axiomatic set theory, transfinite numbers, cardinal numbers, ordinal numbers, modular lattices, Boolean algebras and rings (ordered semigroups, rings, algebras, module, insofar as their order relation is examined) but: geometric lattices see SK 170 Reg .: Axiomatic set theory || Boolean algebra || Boolean ring || Ordered semigroup || Ordered module || Ordered ring || Cardinal number || Set theory || Modular lattice || Ordinal number || Order relation || Structure || Transfinite ordinal number || Association theory
 SK 180 Number theory Rem .: (analytical, elementary, additive, algebraic), stochastic number theory, quadratic forms, valuation theory, Diophantine equations, automorphic forms, sieving methods, (local) bodies, sorrow theory, class field theory, zeta function Usage: (see also SK 240) Reg .: Additive Number Theory || Algebraic Number Theory || Analytical Number Theory || Automorphic Form || Valuation Theory || Diophantine Equation || Elementary Number Theory || Class Field Theory || Body || Kummer Theory || Square Form || Ring | | Sieve method || number theoretic function || number theory || zeta function
 SK 260 Group theory and generalizations Rem .: Representation theory, semigroups, invariant theory, homological methods in group theory, topological groups, Abelian groups, algebraic groups, simple groups, Sylow groups, group rings, Liesche group see SK 340 Usage: (see also SK 340) Reg .: Abelian group || Algebraic group || Representation theory || Simple group || Group ring || Group theory || Semigroup || Homological algebra || Invariant theory || Lie group || Sylow group
 SK 280 General topology General textbooks Rem .: Axiomatics and generalized, topological spaces, weak convergence, function spaces, uniform spaces, metric spaces, standardized spaces, Lindelöf coverage theorem, weak compactness, dimension theory (see also SK 290) (fixed point theories) filter theory (ultrafilter see SK 130) but: Ordered topological vector spaces and mappings see SK 290 Usage: (see also SK 290) Reg .: Axiomatics || Dimension theory || Filter theory || Fixed point theorem || Function space || Ordered topological vector space || Convergence || Textbook || Lindelöf coverage theorem || Metric space || Normalized space || Weak compactness || Weak convergence || Topology || Topological space || Uniform space || Generalized topological space
 SK 320 Homological algebra, sheaf theory Note: categories, functors, algebraic structures, homology theory, cohomology theory, projective resolutions, injective resolutions, spectral sequences. Etalkohomologie, Categorical Algebra Usage: (see also SK 230, SK 340) Reg .: Algebraic structure || Algebraic function field || Etalkohomologie || Functor || Sheaf theory || Homology functor || Homology theory || Homological algebra || Category || Categorical algebra || Cohomology theory || Spectral sequence
 SK 350 Topology and geometry of manifolds, catastrophe theory Rem .: especially differential topology, dynamic systems, geometric topology differentiable manifolds, cobordisms, differentiable mappings, embeddings, immersions, diffeomorphisms (see also SK 370) fiber bundles (see also SK 300) and vector space bundles Characteristic classes, topology of vector and tensor fields (folds) ( see also SK 450, SK 500) Topology of homogeneous spaces (see also SK 340, SK 370), symmetrical spaces, overlapping Usage: (see also SK 300) Reg .: Characteristic class || Diffeomorphism || Differential topology || Differentiable mapping || Differentiable manifold || Dynamic system || Embedding || Fiber bundle || Geometric topology || Homogeneous space || Immersion || Immersion < Topology> || Catastrophe Theory || Cobordism || Manifold || Symmetrical Space || Tensor Field || Topology || Topological Manifold || Overlay || Vector Field || Vector Space Bundle
 SK 370 Differential geometry, tensor analysis Rem .: minimal surfaces, affine and projective differential geometry, non-Euclidean differential geometry, spinor analysis, differentiable manifolds (general theory, definitions), Graßmann manifold, homogeneous manifolds (see also SK 340, SK 350), local Riemannian geometry, Riemannian manifold, Riemannian space, symmetric spaces (see also SK 340, SK 350) submanifolds, isometric embeddings (see also SK 350) convex surfaces, Lorentz group and generalizations, Hermitian and Kähler manifolds (see also SK 780) Finsler spaces and generalizations. Integral geometry, connection Usage: (see also SK 350) Reg .: Affine Differential Geometry || Differential Form || Differential Geometry || Differentiable Manifold || Embedding || Finsler Space || Graßmann Manifold || Homogeneous Manifold || Homogeneous Space || Integral Geometry || Isometric Embedding || Kähler- Manifold || Convex Area || Lorentz Group || Minimal Area || Non-Euclidean Geometry || Projective Differential Geometry || Riemannian Geometry || Riemann Space || Spinor Analysis || Symmetric Space || Tensor Analysis || Submanifold
 SK 380 Classic geometry Rem .: Fundamentals of geometry, analytical geometry, finite geometry, Euclidean geometry, classical algebraic geometry, trigonometry, planimetry, stereometry, affine geometry, descriptive geometry, projective geometry, non-Euclidean geometry, special geometries, convex bodies, geometric inequalities but: general inequalities see SK 490 Reg .: Affine Geometry || Algebraic Geometry || Analytical Geometry || Descriptive Geometry || Finite Geometry || Euclidean Geometry || Planimetry || Projective Geometry || Stereometry || Trigonometry || Inequality
 SK 470 Series, sequences, approximation theory, Rem .: orthogonal series, Hilbert spaces, delta function, convolution, infinite products, infinite fractions, interpolation, iteration Reg .: approximation theory || delta function || factorization || sequence || Hilbert space || interpolation || iteration || orthogonal expansion || series
 SK 600 Functional analysis Rem .: (including distributions, Banach algebras) topological vector space, vector associations, standardized linear spaces, Banach spaces, Hilbert spaces (see also SK 470) other special spaces, spaces of continuous functions, spaces of differentiable and analytical functions, spaces of measurable functions, Lp spaces, Orlicz spaces, Sobolev spaces, embedding theorems distributions and generalized functions, derivatives and differentials of abstract spaces, algebraic topology, Banach algebras, rings and algebras with an involution, "star" algebras (general algebras see SK 230) rings and algebras of operators , "C-star" algebras, operator algebras, "W-star" algebras, group algebras, convolution algebras (see also SK 450) Usage: (Delta function, see also SK 420, SK 450, SK 470) Reg .: Abstract space || Banach algebra || Banach space || C-star algebra || Delta function || Differential operator || Embedding || Convolution || Fixed point theorem || Functional analysis || Functional equation | | Group ring || Hilbert space || integral operator || Lp space || operator algebra || operator equation || operator theory || Orlicz space || space of all continuous functions || ring || Sobolev space || topological vector space || vector lattice || VonNeumann algebra || probability distribution
 SK 800 Probability theory Rem .: Basics, combinatorial probability theory, probability theory on topological groups, geometric probability, distribution theory and characteristic functions, limit theorems, limit distribution theorems, Gaussian error integral Usage: (see also SK 450, SK 470, SK 600; QH 170) Reg .: characteristic function || Gaussian error integral || geometric probability || limit value theorem || combinatorial probability theory || topological group || probability theory || probability distribution
 SK 870 Linear and non-linear optimization Note: semi-finite optimization, fractional optimization, global optimization, vector optimization, convex optimization, parametric optimization but: fixed point algorithms see SK 910 and SK 920, integer optimization see SK 890 stochastic optimization see SK 820, SK 880, SK 970, general textbooks on optimization see SK 970, QH 470, numerical methods of linear algebra see SK 915 Usage: (see also QH 421 linear and non-linear optimization) Reg .: Integer Optimization || Broken Optimization || Global Optimization || Convex Optimization || Linear Optimization || Nonlinear Optimization || Optimization || Semi-Infinite Optimization || Stochastic Optimization || Vector Optimization
 SK 890 Integer and combinatorial optimization, graph theory Note: combinatorial and discrete optimization / programming, mixed integer programming, stochastic and nonlinear integer programming, polyhedral combinatorics, complexity theory, sequence problems (scheduling, routing), graphs, digraphs, hypergraphs, network flows, matroids and independence systems QH 422 integer and combinatorial optimization , QH 450 graphs and networks in general) but: network plan technology see SK 970 and QH 421 Usage: (see also SK 170 combinatorics (classic) Reg .: Digraph || Discrete Optimization || Integer Optimization || Mixed-Integer Optimization || Graph || Graph Theory || Hypergraph || Combinatorial Optimization || Complexity Theory || Matroid || Network Flow || Order Problem || Scheduling || Stochastic Integer Optimization || independence system
 SK 970 Operations Research Note: General textbooks on optimization and operations research, applications in operations research, warehousing, renewal and replacement theory, location planning, network planning technology (CPM, MPM), stochastic network plans, GERT network plans, (stochastic) scheduling problems, modeling and simulation , Queues, reliability theory, see QH 400 Operations Research in general, QH 420 Optimization in general QH 441 Reliability theory QH 443 Queues but: linear and non-linear optimization see SK 870, QH 421, integer optimization see SK 890, QH 422, game theory see SK 860 , QH 430, dynamic optimization see SK 880, QH 423 Reg .: Renewal Theory || Warehousing || Textbook || Modeling || Network Planning || Operations Research || Optimization || Scheduling || Queue || Reliability Theory