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36 relations: Arthur Moritz Schoenflies, Borel set, Bronisław Knaster, Cantor set, Compact space, Composant, Connected space, Continuum (topology), Counterexample, Dense set, Dynamical system, Fundamenta Mathematicae, General topology, George David Birkhoff, Hausdorff distance, Hilbert cube, Horseshoe map, Indecomposability, Inverse limit, K-cell (mathematics), Kunizo Yoneyama, L. E. J. Brouwer, Lakes of Wada, Marcy Barge, Marie Charpentier, Metric (mathematics), Metric space, N-sphere, Pseudo-arc, Sierpinski carpet, Solenoid (mathematics), Stefan Mazurkiewicz, Takeo Wada, Topologist's sine curve, Warsaw School (mathematics), Zygmunt Janiszewski.
Arthur Moritz Schoenflies
Arthur Moritz Schoenflies (17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
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Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.
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Bronisław Knaster
Bronisław Knaster (22 May 1893 – 3 November 1980) was a Polish mathematician; from 1939 a university professor in Lwów and from 1945 in Wrocław.
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Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Composant
In point-set topology, the composant of a point p in a continuum A is the union of all proper subcontinua of A that contain p. If a continuum is indecomposable, then its composants are pairwise disjoint.
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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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Continuum (topology)
In the mathematical field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff space.
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Counterexample
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.
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Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Fundamenta Mathematicae
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.
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General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
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George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem.
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Hausdorff distance
In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other.
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Hilbert cube
In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology.
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Horseshoe map
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself.
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Indecomposability
In constructive mathematics, indecomposability or indivisibility (Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces.
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Inverse limit
In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.
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K-cell (mathematics)
A k-cell is a higher-dimensional version of a rectangle or rectangular solid.
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Kunizo Yoneyama
Kunizo Yoneyama (1877–1968) was a Japanese mathematician at Kyoto University working in topology.
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L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.
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Lakes of Wada
In mathematics, the are three disjoint connected open sets of the plane or open unit square with the counterintuitive property that they all have the same boundary.
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Marcy Barge
Marcy Barge is a professor of mathematics at Montana State University.
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Marie Charpentier
Marie Charpentier (1903–1994) was the first woman to obtain a doctorate in pure mathematics in France, and the second woman, after Marie-Louise Dubreil-Jacotin, to obtain a faculty position in mathematics at a university in France.
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Metric (mathematics)
In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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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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Pseudo-arc
In general topology, the pseudo-arc is the simplest nondegenerate hereditarily indecomposable continuum.
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Sierpinski carpet
The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916.
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Solenoid (mathematics)
In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each Si is a circle and fi is the map that uniformly wraps the circle Si+1 ni times (ni ≥ 2) around the circle Si.
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Stefan Mazurkiewicz
Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability.
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Takeo Wada
was a Japanese mathematician at Kyoto University working in analysis and topology.
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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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Warsaw School (mathematics)
Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis.
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Zygmunt Janiszewski
Zygmunt Janiszewski (June 12, 1888 – January 3, 1920) was a Polish mathematician.
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Decomposable continuum, Indecomposable continua, Knaster continuum.
References
[1] https://en.wikipedia.org/wiki/Indecomposable_continuum
