KnowraQuotient spaceLinked fromLinked fromThe 13 pages that link to Quotient space, each with the reason it gives.All 13Broader topic 3Related 10Vector spaceBroader topic: Quotients collapse a subspace to zero while preserving vector-space operations.Homogeneous coordinatesRelated: Projective space is built from nonzero vectors after identifying vectors on the same line.Configuration spaceRelated: Forgetting point labels identifies configurations related by permutations.Quotient groupRelated: It uses the same class-collapsing idea but need not preserve a group operation.Rank–nullity theoremRelated: The map’s image is isomorphic to the domain modulo its kernel.Invariant subspaceRelated: An invariant subspace lets the operator induce a map on the quotient.Kernel (linear algebra)Related: Factoring the domain by the kernel identifies inputs with the same output.Equivalence classBroader topic: Its points are classes, and its topology is defined from the original space.Open mapping theoremRelated: The theorem makes quotient maps by closed subspaces open, a key structural property.Partition of a setBroader topic: Its identifications group points into partition-like equivalence classes.Flat torusRelated: Identifying lattice translates turns the plane into a compact torus.Dimension theorem for vector spacesRelated: The map induces an isomorphism from the domain modulo its kernel onto its image.Excision theoremRelated: Under suitable conditions, relative homology can be computed using a quotient by the subspace.