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31 relations: Adolf Hurwitz, Classifying space, Configuration space (physics), Connected space, Cubical complex, Degree (graph theory), Discrete group, Eilenberg–MacLane space, Emil Artin, Fundamental group, Graph (topology), Group action, Homeomorphism, Homotopy, Joan Birman, Lens space, Massey product, Mathematics, Moduli space, Non-positive curvature, Orbifold, Phase space, Ran space, Retract, Robert Ghrist, Simply connected space, State space, State space (physics), Symmetric group, Topological space, Tuple.
Adolf Hurwitz
Adolf Hurwitz (26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory.
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Classifying space
In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle EG → BG.
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Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.
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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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Cubical complex
In mathematics, a cubical complex or cubical set is a set composed of points, line segments, squares, cubes, and their ''n''-dimensional counterparts.
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Degree (graph theory)
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice.
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Discrete group
In mathematics, a discrete subgroup of a topological group G is a subgroup H such that there is an open cover of G in which every open subset contains exactly one element of H; in other words, the subspace topology of H in G is the discrete topology.
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Eilenberg–MacLane space
In mathematics, and algebraic topology in particular, an Eilenberg–MacLane spaceSaunders Mac Lane originally spelt his name "MacLane" (without a space), and co-published the papers establishing the notion of Eilenberg–MacLane spaces under this name.
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Emil Artin
Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.
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Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
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Graph (topology)
In topology, a subject in mathematics, a graph is a topological space which arises from a usual graph G.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
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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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Joan Birman
Joan Sylvia Lyttle Birman (born May 30, 1927 in New York CityLarry Riddle. "", Biographies of Women Mathematicians, at Agnes Scott College) is an American mathematician, specializing in braid theory and knot theory.
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Lens space
A lens space is an example of a topological space, considered in mathematics.
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Massey product
In algebraic topology, the Massey product is a cohomology operation of higher order introduced in, which generalizes the cup product.
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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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Moduli space
In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.
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Non-positive curvature
In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry.
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Orbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold.
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Phase space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.
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Ran space
In mathematics, the Ran space (or Ran's space) of a topological space X is a topological space \operatorname(X) whose underlying set is the set of all nonempty finite subsets of X: for a metric space X the topology is induced by the Hausdorff distance.
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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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Robert Ghrist
Robert W. Ghrist (born 1969) is an American mathematician, known for his work on topological methods in applied mathematics.
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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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State space
In the theory of discrete dynamical systems, a state space is the set of all possible configurations of a system.
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State space (physics)
In physics, a state space is an abstract space in which different "positions" represent, not literal locations, but rather states of some physical system.
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Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
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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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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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References
[1] https://en.wikipedia.org/wiki/Configuration_space_(mathematics)
