adj
(topology, of a topological space) Having a singleton as its fundamental group.
n
(mathematics) A kind of topological space.
n
(topology) A topological space, looked at in relation to one of its covering spaces, fibrations, or bundles.
n
(topology, algebraic topology) Any of a sequence of numbers, denoted bₙ, which characterise a given topological space K by giving, for each dimension, the number of holes in K of said dimension; (formally) the rank of the nth homology group, Hₙ, of K.
n
(mathematics) The set of all bounded subsets of a topological vector space
n
In a simplicial chain complex: A group homomorphism induced by mapping each oriented k-simplex to a formal sum with alternating signs of the oriented (k − 1)-simplices which are faces of the said k-simplex.
n
(topology) A theorem which (in one of its simplest forms) states that a continuous function from an n-dimensional unit cube (in ℝⁿ) to itself has a fixed point.
n
(mathematics) An isomorphism in the contact category.
adj
(mathematics) dual to something semisimple.
n
(mathematics, uncommon) Synonym of hyperbolic cosine.
n
(linear algebra) An explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
n
(topology, specifically) The same, but with the manifold in question being the 3-dimensional sphere.
n
(linear algebra) An element on the main diagonal of a square matrix, that is, an element in row k and column k where k is an integer between 1 and the number of rows (or columns) in the matrix.
adj
(mathematics) Converted into a diagonal matrix
n
(more formally) a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).
adj
(mathematics, physics) Exhibiting duality.
n
(mathematics) The set of all real, square symmetric matrices whose diagonal entries are all equal to one and whose eigenvalues are all non-negative.
adj
(mathematics, of a network) That is in contact with an internal network
adj
(mathematics) Pertaining to topological spaces that are Cartesian closed categories.
n
(mathematics, geometry) A space where the principles of Euclidean geometry apply.
n
(algebra) A sequence of groups with adjacent groups connected by homomorphisms such that the image of one homomorphism is the kernel of the next.
n
(algebraic topology) A continuous mapping satisfying the homotopy lifting property with respect to any space.
n
(topology) Given a set X, a family of topological spaces (M_i,T_i)_(i∈I) and a family of functions f_i:M_i→X, the final topology is the finest topology on X such that all f_i are continuous.
n
A mathematician who specializes in geometric topology.
n
(group theory) A mapping of a mathematical group to the permutations of an object that is compatible with the group operation.
adj
(topology, of a 3-manifold) Irreducible, compact, and containing a non-∂-parallel incompressible surface (besides a sphere or disk).
adj
(mathematics) Invariant relative to a proper orthogonal group.
n
(topology) a continuous bijection from one topological space to another, with continuous inverse.
adj
(mathematics) Having to do with homology.
n
(algebraic topology) The quotient group of the kth cycle group modulo the kth boundary group (derived from the chain complex of, e.g., a given simplicial complex).
n
(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point.
n
Any of a group of structures related by homotopy
v
(topology, transitive) More loosely, to exhibit a homotopy equivalence between two spaces.
adj
(topology, of two continuous maps) Such that there is a homotopy (a continuous deformation) taking one to the other.
adj
(mathematics) homotopic
n
(topology) A theory associating a system of groups with each topological space.
n
(mathematics) The systematic study of the situation of maps' having a homotopy between them; the study of equivalence classes (called homotopy classes) of maps.
adj
(mathematics) Invariant for any transformation that commutes with a specified endomorphism.
n
(mathematics) A mapping from operators to operators.
n
(logic, physics) A generalisation of a property (or sets of properties)
n
(calculus) A differential operator that preserves mathematical smoothness.
adj
(mathematics) Analogous to plactic, generalized to the theory of noncommutative symmetric functions.
n
(topology) a quotient map
v
(topology, transitive) To define or demonstrate an isotopy of (one map with another).
n
(mathematics) A form of homotopy that is always an embedding.
n
(topology) Any group that is a smooth manifold and whose group operations are differentiable.
n
(topology) A topological group whose underlying topology is both locally compact and Hausdorff.
n
(physics, mathematics) The group of all Lorentz transformations in spacetime.
n
(mathematics) A theory combining mereology and topology, investigating relations between parts and wholes and boundaries between them.
n
(differential geometry) a symmetric bilinear form which is non-degenerate (i.e., having all non-zero eigenvalues); a differential of distance on a manifold
adj
(mathematics) "Thickened" using formal canonical relations between the cotangent bundles of smooth manifolds.
n
(topology) An automorphism that induces a set of Dehn twists around a surface.
n
(mathematics) A bounded linear operator having a norm equal to its spectral radius.
adj
(algebra, mathematical analysis) Of a mathematical structure, endowed with a norm.
adj
(topology, of a map) Homotopic to a constant map.
adj
(topology, of a map) Homotopic to a constant map.
adj
(topology, of a map) Homotopic to a constant map.
adj
(mathematics) Having a natural family of distributive morphisms and an identity morphism that are coherent.
n
(physics) An oriented generalization of an orbifold
n
(topology) Any of a set of ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homoeomorphic manifold.
adj
(mathematics) Describing a form of parabolic Iwahori subgroups
adj
(of a topological space) Such that every pair of points in the space comprises the boundary of some path mapped to the space continuously.
n
(mathematics) An approach to topology that avoids mentioning points.
n
(mathematics) A metrizable space together with an equivalence class of sc-smooth structures.
n
(mathematics) The field of study of pretopological spaces (in plural for different prespaces).
n
(of a knot k) That no nontrivial Dehn surgery along k in the 3-sphere yields a simply connected manifold.
n
(computer graphics) Synonym of retopology
n
(mathematics, linear algebra) The field (algebraic structure) for which scalar multiplication is defined for a given vector space; field of scalars.
n
(by generalisation) the enumerative geometry of linear subspaces; the study of analogous questions in generalised cohomology theories.
n
(topology) An ordering of the facets of a boundary complex such that the intersection of each facet (other than the first) with the union of all preceding facets is homeomorphic to a ball or sphere. See Shelling (topology)
n
(crystallography, mineralogy) The set of all symmetry operations that can be applied to a given crystal without changing it.
n
Alternative spelling of space group [(crystallography, mineralogy) The set of all symmetry operations that can be applied to a given crystal without changing it.]
v
(mathematics) To generate an entire space by means of linear combinations.
adj
(topology) Having a subspace of hypercyclic vectors
n
(mathematics) A differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds
n
(physics) A generalization of groups, used in the study of supersymmetry.
adj
(group theory, of a group) Whose characteristic abelian subgroups are cyclic.
n
(mathematics, linear algebra) A relation between generators of a module.
n
(mathematics) A type of mapping on polynomials that may be defined by means of field theory as the transformation on minimal polynomials implied by a different choice of primitive element.
Note: Concept clusters like the one above are an experimental OneLook
feature. We've grouped words and phrases into thousands of clusters
based on a statistical analysis of how they are used in writing. Some
of the words and concepts may be vulgar or offensive. The names of the
clusters were written automatically and may not precisely describe
every word within the cluster; furthermore, the clusters may be
missing some entries that you'd normally associate with their
names. Click on a word to look it up on OneLook.
Our daily word games Threepeat and Compound Your Joy are going strong. Bookmark and enjoy!
Today's secret word is 8 letters and means "Believable and worthy of trust." Can you find it?