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# N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the. 

## Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

## Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

## Computer graphics

Computer graphics are pictures and films created using computers.

## CW complex

In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.

## Discrete space

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.

## Filtration (mathematics)

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

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.

## Homotopical algebra

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.

## Hypercovering

In mathematics, and in particular homotopy theory, a hypercovering (or hypercover) is a simplicial object that generalises the Čech nerve of a cover.

## Image functors for sheaves

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

Mathematical induction is a mathematical proof technique.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Nerve (category theory)

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.

## Obstruction theory

In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants.

## Peter McMullen

Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.

## Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

## Pullback (category theory)

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.

## Simplicial complex

In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).

## Simplicial set

In mathematics, a simplicial set is an object made up of "simplices" in a specific way.

## Spectral sequence

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.

## Subspace topology

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).

## Tesseract

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.

## Topological graph

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.

## Topological skeleton

In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries.

## Topological space

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.

## References

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