26 relations: Algebraic geometry, Algebraic topology, Computer graphics, CW complex, Discrete space, Filtration (mathematics), Geometry, Homotopical algebra, Hypercovering, Image functors for sheaves, Mathematical induction, Mathematics, Nerve (category theory), Obstruction theory, Peter McMullen, Polytope, Pullback (category theory), Simplicial complex, Simplicial set, Spectral sequence, Springer Science+Business Media, Subspace topology, Tesseract, Topological graph, Topological skeleton, Topological space.
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
Computer graphics are pictures and films created using computers.
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.
In mathematics, a filtration \mathcal is an indexed set S_i of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that If the index i is the time parameter of some stochastic process, then the filtration can be interpreted as representing all historical but not future information available about the stochastic process, with the algebraic object S_i gaining in complexity with time.
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
In mathematics, homotopical algebra is a collection of concepts comprising the nonabelian aspects of homological algebra as well as possibly the abelian aspects as special cases.
In mathematics, and in particular homotopy theory, a hypercovering (or hypercover) is a simplicial object that generalises the Čech nerve of a cover.
In mathematics, especially in sheaf theory, a domain applied in areas such as topology, logic and algebraic geometry, there are four image functors for sheaves which belong together in various senses.
Mathematical induction is a mathematical proof technique.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory.
In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants.
Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.
In elementary geometry, a polytope is a geometric object with "flat" sides.
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms and with a common codomain.
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
In mathematics, a simplicial set is an object made up of "simplices" in a specific way.
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations.
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
In mathematics, a topological graph is a representation of a graph in the plane, where the ''vertices'' of the graph are represented by distinct points and the ''edges'' by Jordan arcs (connected pieces of ''Jordan curves'') joining the corresponding pairs of points.
In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries.
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.