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36 relations: Cambridge University Press, Collapse (topology), Comb space, Cone (topology), Connected space, CW complex, Dunce hat (topology), Euclidean space, Hawaiian earring, Hilbert space, Homotopy, Homotopy group, House with two rooms, Identity function, If and only if, Kuiper's theorem, Locally connected space, Locally simply connected space, Manifold, Mathematics, N-connected space, N-sphere, Neighbourhood (mathematics), Neighbourhood system, Prentice Hall, Reduced homology, Retract, Shape theory (mathematics), Simply connected space, Singular homology, Star domain, Topological space, Topologist's sine curve, Trivial group, Unit sphere, Whitehead manifold.
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Collapse (topology)
In topology, a branch of mathematics, a collapse reduces a simplicial complex (or more generally, a CW complex) to a homotopy-equivalent subcomplex.
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Comb space
In mathematics, particularly topology, a comb space is a subspace of \R^2 that looks rather like a comb.
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Cone (topology)
In topology, especially algebraic topology, the cone CX of a topological space X is the quotient space: of the product of X with the unit interval I.
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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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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Dunce hat (topology)
In topology, the dunce hat is a compact topological space formed by taking a solid triangle and gluing all three sides together, with the orientation of one side reversed.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Hawaiian earring
In mathematics, the Hawaiian earring H is the topological space defined by the union of circles in the Euclidean plane R2 with center (0) and radius for.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.
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House with two rooms
House with two rooms or Bing's house is a particular contractible, 2-dimensional simplicial complex that is not collapsible.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Kuiper's theorem
In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H.
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Locally connected space
In topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets.
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Locally simply connected space
In mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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N-connected space
In the mathematical branch of algebraic topology, specifically homotopy theory, n-connectedness (sometimes, n-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness.
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N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Neighbourhood system
In topology and related areas of mathematics, the neighbourhood system, complete system of neighbourhoods, or neighbourhood filter \mathcal(x) for a point x is the collection of all neighbourhoods for the point x.
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Prentice Hall
Prentice Hall is a major educational publisher owned by Pearson plc.
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Reduced homology
In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero.
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Retract
In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace which preserves the position of all points in that subspace.
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Shape theory (mathematics)
Shape theory is a branch of topology, which provides a more global view of the topological spaces than homotopy theory.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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Singular homology
In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X).
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Star domain
In mathematics, a set S in the Euclidean space Rn is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an x0 in S such that for all x in S the line segment from x0 to x is in S. This definition is immediately generalizable to any real or complex vector space.
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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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Topologist's sine curve
In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example.
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Trivial group
In mathematics, a trivial group is a group consisting of a single element.
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Unit sphere
In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.
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Whitehead manifold
In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to R3.
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Contractible, Contractible topological space, Locally contractible, Locally contractible space.
References
[1] https://en.wikipedia.org/wiki/Contractible_space
