User:Soobtoob/Books/Mathematical Structures

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Mathematical Structures

Set Theory: Set (mathematics); Naive set theory; Set theory; Element (mathematics); Subset; Union (set theory); Intersection (set theory); Complement (set theory); Symmetric difference; Partition of a set; Singleton (mathematics); Empty set; Ordered pair; Cartesian product; Binary relation; Binary operation; Power set; Sequence; Closure (mathematics); Image (mathematics); Finite set; Ordered set; Cardinal number; Ordinal number; Limit ordinal; Successor ordinal; Class (set theory); Von Neumann universe; Equivalence class; Equivalence relation; Infinite set; Aleph number; Beth number; Measurable cardinal; Large cardinal; Inaccessible cardinal; Function (mathematics); Map (mathematics); Homomorphism; Homeomorphism; Diffeomorphism
Algebraic Structures: Magma (algebra); Commutative property; Associative property; Distributive property; Power associativity; Identity element; Inverse element; Idempotence; Unipotent; Absorption law; Alternativity; Medial; Cancellation property; Groupoid; Semigroup; Inverse semigroup; Quasigroup; Monoid; Group (mathematics); Abelian group; Semiring; Ring (mathematics); Commutative ring; Integral domain; Division ring; Nonassociative ring; Field (mathematics); Ordered field; Quasifield; Real number; Topological group; Lie group; Module (mathematics); Free module; Vector space; Algebra (ring theory); Lie algebra; Associative algebra; Unique factorization domain; Principal ideal domain; Euclidean domain; BCK algebra; Band (mathematics); Directed graph; Residuated lattice; Boolean algebra; Relation algebra; Modal algebra; Cylindric algebra
Order Structures: Preorder; Strict weak ordering; Total order; Trichotomy; Extended real number line; Antichain; Partially ordered set; Hasse diagram; Directed acyclic graph; Duality (order theory); Product order; Greatest element; Maximal element; Upper and lower bounds; Supremum; Infimum; Limit superior and limit inferior; Cofinal (mathematics); Linked set; Directed set; Centered set; Net (mathematics); Upper set; Ideal (order theory); Filter (mathematics); Ultrafilter; Completeness (order theory); Dense order; Distributivity (order theory); Distributive lattice; Completely distributive lattice; Ascending chain condition; Infinite descending chain; Countable chain condition; Knaster's condition; Well-order; Well-founded relation; Well-quasi-ordering; Semilattice; Complete partial order; Bounded complete poset; Complete lattice; Knaster–Tarski theorem; Infinite divisibility; Heyting algebra; Complete Heyting algebra; Pointless topology; Boolean algebra (structure); Boolean ring; Kleene algebra; Complete Boolean algebra; Complemented lattice; Quantale; Partially ordered group; Archimedean property; Ordered ring; Artinian; Noetherian; Linearly ordered group; Monomial order; Inversion (discrete mathematics); Incidence algebra; Domain theory; Scott domain; Scott information system; Power domains; Scott continuity; Compact element; Lattice (order); Lindenbaum–Tarski algebra; Tree (set theory)
Topological Structure: Topological space; Disjoint union (topology); Product topology; Subspace topology; Quotient space; Topological tensor product; Open set; Closed set; Clopen set; Closure (topology); Boundary (topology); Dense set; Gδ set; Fσ set; Closeness (mathematics); Neighbourhood (mathematics); Continuous function; Local homeomorphism; Open and closed maps; Germ (mathematics); Base (topology); Subbase; Cover (topology); Covering space; Atlas (topology); Limit point; Baire category theorem; Nowhere dense set; Baire space; Banach–Mazur game; Meagre set; Compact space; Relatively compact subspace; Heine–Borel theorem; Tychonoff's theorem; Finite intersection property; Compactification; Measure of non-compactness; Paracompact space; Locally compact space; Compactly generated space; Axiom of countability; Sequential space; First-countable space; Second-countable space; Separable space; Lindelöf space; Σ-compact space; Connected space; Separation axiom; Kolmogorov space; T1 space; Hausdorff space; Completely Hausdorff space; Regular space; Tychonoff space; Normal space; Urysohn's lemma; Tietze extension theorem; Separated sets; Topological algebra; Topological ring; Topological module; Topological abelian group; Simply connected space; Semi-locally simply connected; Path (topology); Homotopy; Homotopy lifting property; Pointed space; Wedge sum; Smash product; Cone (topology); Adjunction space; Discrete space; Locally constant function; Trivial topology; Cofiniteness; Comparison of topologies; Restricted product; Unit interval; Continuum (topology); Long line (topology); Cantor set; Cantor space; Space-filling curve; Uniform norm; Weak topology; Strong topology; Lower limit topology; Real tree; Compact-open topology; Solenoid (mathematics)
Group Structure: Subgroup; Normal subgroup; Quotient group; Group homomorphism; Semidirect product; Direct product of groups; Kernel (algebra); Direct sum of groups; Wreath product; Simple group; Finite group; Infinite group; Multiplicative group; Group scheme; Cyclic group; Dihedral group; Nilpotent group; Solvable group; Symmetric group; Alternating group; Mathieu group; Conway group; Janko group J1; Hall–Janko group; Janko group J3; Janko group J4; Fischer group; Baby Monster group; Monster group; Discrete group; Lattice (discrete subgroup); Integer; Lattice (group); Modular group; Circle group; General linear group; Special linear group; Orthogonal group; Unitary group; Special unitary group; Symplectic group; G2 (mathematics); F4 (mathematics); E6 (mathematics); E7 (mathematics); E8 (mathematics); Lorentz group; Poincaré group; Conformal group; Loop group; Algebraic group; Elliptic curve; Linear algebraic group; Abelian variety
Metric Structure: Metric space; Metric (mathematics); Isometry; Contraction mapping; Metric map; Norm (mathematics); Measure (mathematics); Taxicab geometry; Ultrametric space; P-adic number; P-adic analysis; Ball (mathematics); Bounded set; Pointwise convergence; Metrization theorem; Complete metric space; Cauchy sequence; Banach fixed-point theorem; Polish space; Hausdorff distance; Intrinsic metric; Injective metric space; Isomorphism; Monomorphism; Epimorphism; Tensor product; Direct sum of modules; Direct product; Linear subspace; Quotient space (linear algebra); Eigenvalues and eigenvectors; Endomorphism; Injective function; Surjective function; Function composition; Linear map; Linear equation; System of linear equations; Linear algebra; Matrix (mathematics); Determinant; Matrix multiplication
Differential Structure: Differential structure; Topological manifold; Differentiable manifold; Differential calculus; Smooth function; Holomorphic function; Tangent space; Vector field; Tensor field; Exterior derivative; Differential geometry; Smooth structure; Analytic function; Complex number; Nash embedding theorem; Algebraic geometry and analytic geometry; Algebraic variety; Biholomorphism; Pseudogroup; Symplectomorphism; Möbius transformation; Affine transformation; Sheaf (mathematics); Functor; Pullback; Ringed space; Scheme (mathematics); Local ring; Maximal ideal; Complex analytic geometry; Synthetic differential geometry; Cotangent space; Cotangent bundle; Taylor series; Jet (mathematics); Completion (ring theory); Tangent bundle; Dual number; Derivative; Chain rule; Directional derivative; Curve; Linear functional; Support (mathematics); Locally finite collection; Function space; Lp space; Sobolev space; Real line; Lagrangian; Dual space; Hamiltonian mechanics; Fiber bundle; Symplectic manifold; Infinitesimal; Exact differential; Tensor bundle; Tensor; Frame bundle; Jet bundle; Differential operator; Jet group; Connection (mathematics); Multivariable calculus; Implicit function; Inverse function theorem; Lie derivative; Affine connection; Integral; Differential form; Green's theorem; Divergence theorem; Stokes' theorem; Submanifold; Pushforward (differential); Sard's theorem; Gradient; Divergence; Curl (mathematics); Exterior algebra; Product rule; Surface; 3-manifold; 4-manifold; E8 manifold; Riemannian manifold; Inner product space; Riemann curvature tensor; Pseudo-Riemannian manifold; Metric tensor; Metric signature; Definite quadratic form; Finsler manifold; Almost complex manifold; Riemann surface; Manifold; Frölicher space; Orbifold; Rectifiable set; Arc length; Diffeology; Limit (mathematics); Series (mathematics); Power rule; Fundamental theorem of calculus; Law of Continuity; Limits of integration; Partial derivative; Non-standard analysis; Graph of a function; (ε, δ)-definition of limit; Limit of a sequence; Limit of a function; Derivative of a constant; Sum rule in differentiation; Constant factor rule in differentiation; Linearity of differentiation; Quotient rule; Inverse functions and differentiation; Antiderivative; Sum rule in integration; Constant factor rule in integration; Linearity of integration; Integration by parts; Constant of integration; Integration by substitution; Weierstrass substitution; Differentiation under the integral sign; Trigonometric substitution; Natural logarithm; E (mathematical constant); Exponential function; Linear function; Secant; Slope; Tangent; Concave function; Finite difference; Radian; Factorial; Binomial theorem; Free variables and bound variables