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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. [1]

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

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

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Algebraic topology

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

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Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

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Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

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Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

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Christmas traditions

Christmas traditions vary from country to country.

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Computer graphics

Computer graphics are pictures and films created using computers.

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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.

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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.

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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.

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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.

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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.

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

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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.

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Mathematical induction

Mathematical induction is a mathematical proof technique.

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

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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.

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New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

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New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

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New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

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Obstruction theory

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

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Peter McMullen

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

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

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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.

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Simplicial complex

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

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Simplicial set

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

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Spectral sequence

In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations.

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Springer Science+Business Media

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.

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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).

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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.

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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.

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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.

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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.

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2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

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2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

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Redirects here:

0-coskeleton, 0-skeleton, 1-coskeleton, 1-skeleton, Coskeleton, D-skeleton, N-coskeleton, Skeletal filtration, Skeleton (topology).


[1] https://en.wikipedia.org/wiki/N-skeleton

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