Geometry And Topology
28 entries in the Geometry And Topology compendium.
Affine geometryGeometry without distance or angle, focusing on parallelism.Affine spaceGeometric structure preserving parallelism and ratios, not distances.Affine transformationA transformation preserving lines and parallelism in affine spaces.Algebraic geometryBranch of mathematics studying zeros of polynomial equations.Algebraic topologyBranch of mathematics using algebra to study topological spaces.Analytic geometryStudy of geometry using a coordinate system.AngleA geometric figure formed by two lines meeting at a point.Cartesian coordinate systemCoordinate system using perpendicular axes to locate points.Congruence (geometry)Two figures are congruent if they have identical shape and size.Convex setA set containing all line segments between its points.Coordinate systemA system using numbers to determine positions in space.CoplanarityCoplanarity determines if points or lines share a common plane.Compact spaceCompactness makes a space behave like a finite set.Connected spaceA topological space that cannot be split into two disjoint open subsets.Basis (linear algebra)A basis is a linearly independent spanning set of a vector space.Cartesian productSet of all ordered pairs from two sets.Closure (mathematics)Closure is the smallest superset closed under given operations.Braid theoryStudy of braid groups and their applications.CohomologyAlgebraic invariants encoding obstructions to global properties.Differential geometryStudy of smooth shapes and spaces using calculus and algebra.FractalGeometric shapes with self-similarity and non-integer fractal dimension.Graph embeddingGraph embedding: drawing a graph on a surface without crossing edges.Homology (mathematics)Homology studies invariants via chain complexes and cycles.Knot theoryMathematical study of knots as embeddings of circles in space.ManifoldA topological space locally resembling Euclidean space near each point.Metric spaceA set with a distance function between its points.Topological spaceA set with a structure defining closeness without distance.TorusA surface of revolution shaped like a doughnut.
Browse Geometry And Topology in the interactive codex →