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26 relations: Acta Mathematica, American Mathematical Society, Base (topology), Cantor set, CAT(k) space, Compact Riemann surface, Compact space, Complete metric space, Connected space, End (topology), Equivalence class, Geometric group action, Glossary of Riemannian and metric geometry, Homeomorphism, Hyperbolic group, Hyperbolic space, Isometry, Menger sponge, Metrization theorem, Mikhail Leonidovich Gromov, Neighbourhood system, Point at infinity, Quasi-isometry, Real line, Sphere, Tree (graph theory).
Acta Mathematica
Acta Mathematica is a peer-reviewed open-access scientific journal covering research in all fields of mathematics.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Base (topology)
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set.
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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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CAT(k) space
In mathematics, a \mathbf space, where k is a real number, is a specific type of metric space.
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Compact Riemann surface
In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space.
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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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Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
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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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End (topology)
In topology, a branch of mathematics, the ends of a topological space are, roughly speaking, the connected components of the "ideal boundary" of the space.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Geometric group action
In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.
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Glossary of Riemannian and metric geometry
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
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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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Hyperbolic group
In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.
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Hyperbolic space
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.
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Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
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Menger sponge
In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve.
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Metrization theorem
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
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Mikhail Leonidovich Gromov
Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.
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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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Point at infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
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Quasi-isometry
In mathematics, quasi-isometry is an equivalence relation on metric spaces that ignores their small-scale details in favor of their coarse structure.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Tree (graph theory)
In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.
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References
[1] https://en.wikipedia.org/wiki/Gromov_boundary
