[{"n": "Affine geometry", "u": "/e/geometry-and-topology/affine-geometry/", "s": "Geometry without distance or angle, focusing on parallelism."}, {"n": "Affine space", "u": "/e/geometry-and-topology/affine-space/", "s": "Geometric structure preserving parallelism and ratios, not distances."}, {"n": "Affine transformation", "u": "/e/geometry-and-topology/affine-transformation/", "s": "A transformation preserving lines and parallelism in affine spaces."}, {"n": "Algebraic geometry", "u": "/e/geometry-and-topology/algebraic-geometry/", "s": "Branch of mathematics studying zeros of polynomial equations."}, {"n": "Algebraic topology", "u": "/e/geometry-and-topology/algebraic-topology/", "s": "Branch of mathematics using algebra to study topological spaces."}, {"n": "Analytic geometry", "u": "/e/geometry-and-topology/analytic-geometry/", "s": "Study of geometry using a coordinate system."}, {"n": "Angle", "u": "/e/geometry-and-topology/angle/", "s": "A geometric figure formed by two lines meeting at a point."}, {"n": "Congruence (geometry)", "u": "/e/geometry-and-topology/congruence-geometry/", "s": "Two figures are congruent if they have identical shape and size."}, {"n": "Convex set", "u": "/e/geometry-and-topology/convex-set/", "s": "A set containing all line segments between its points."}, {"n": "Coordinate system", "u": "/e/geometry-and-topology/coordinate-system/", "s": "A system using numbers to determine positions in space."}, {"n": "Coplanarity", "u": "/e/geometry-and-topology/coplanarity/", "s": "Coplanarity determines if points or lines share a common plane."}, {"n": "Compact space", "u": "/e/geometry-and-topology/compact-space/", "s": "Compactness makes a space behave like a finite set."}, {"n": "Connected space", "u": "/e/geometry-and-topology/connected-space/", "s": "A topological space that cannot be split into two disjoint open subsets."}, {"n": "Basis (linear algebra)", "u": "/e/geometry-and-topology/basis-linear-algebra/", "s": "A basis is a linearly independent spanning set of a vector space."}, {"n": "Cartesian product", "u": "/e/geometry-and-topology/cartesian-product/", "s": "Set of all ordered pairs from two sets."}, {"n": "Closure (mathematics)", "u": "/e/geometry-and-topology/closure-mathematics/", "s": "Closure is the smallest superset closed under given operations."}, {"n": "Braid theory", "u": "/e/geometry-and-topology/braid-theory/", "s": "Study of braid groups and their applications."}, {"n": "Cohomology", "u": "/e/geometry-and-topology/cohomology/", "s": "Algebraic invariants encoding obstructions to global properties."}, {"n": "Differential geometry", "u": "/e/geometry-and-topology/differential-geometry/", "s": "Study of smooth shapes and spaces using calculus and algebra."}, {"n": "Fractal", "u": "/e/geometry-and-topology/fractal/", "s": "Geometric shapes with self-similarity and non-integer fractal dimension."}, {"n": "Graph embedding", "u": "/e/geometry-and-topology/graph-embedding/", "s": "Graph embedding: drawing a graph on a surface without crossing edges."}, {"n": "Homology (mathematics)", "u": "/e/geometry-and-topology/homology-mathematics/", "s": "Homology studies invariants via chain complexes and cycles."}, {"n": "Knot theory", "u": "/e/geometry-and-topology/knot-theory/", "s": "Mathematical study of knots as embeddings of circles in space."}, {"n": "Manifold", "u": "/e/geometry-and-topology/manifold/", "s": "A topological space locally resembling Euclidean space near each point."}, {"n": "Metric space", "u": "/e/geometry-and-topology/metric-space/", "s": "A set with a distance function between its points."}, {"n": "Topological space", "u": "/e/geometry-and-topology/topological-space/", "s": "A set with a structure defining closeness without distance."}, {"n": "Torus", "u": "/e/geometry-and-topology/torus/", "s": "A surface of revolution shaped like a doughnut."}]