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{{short description|Characterizes sets of lattices that are bounded in a certain sense}} ...nvention used in naming compactness theorems, because they were formulated in terms of [[sequential compactness]] (the possibility of selecting a converg ...

{{short description|One of several theorems in different areas of mathematics}} ...ry]], '''Schur's theorem''' is a theorem of [[:de:Axel Schur|Axel Schur]]. In [[functional analysis]], '''Schur's theorem''' is often called [[Schur's pr ...

...athbb{H}^3 / \Gamma</math> where <math>\Gamma</math> is a [[discrete group|discrete subgroup]] of PSL(2,'''C'''). Here, the subgroup <math>\Gamma</math>, a [[K ...f a group action of a Kleinian group on the space. A Kleinian group is any discrete subgroup, consisting only of [[Isolated point|isolated points]], of orienta ...

...ann surface]]s, or, more generally, [[algebraic curve]]s, ''X'' and ''Y'', in the case of [[genus (mathematics)|genus]] ''g'' > 1. The simplest is that t ...renced as the De Franchis-[[Francesco Severi|Severi]] theorem. It was used in an important way by [[Gerd Faltings]] to prove the [[Mordell conjecture]]. ...

{{Short description|1=Overview of and topical guide to discrete mathematics}} ...screteMathematics}}</ref> Discrete mathematics, therefore, excludes topics in "continuous mathematics" such as [[calculus]] and [[Mathematical analysis|a ...

{{Short description|Branch of geometry}} ...e geometry]], [[functional analysis]], [[geometry of numbers]], [[integral geometry]], [[linear programming]], [[probability theory]], [[game theory]], etc. ...

{{Short description|Geometry without the parallel postulate}} {{General geometry}} ...

...ption|On lower bounds on the number of lines determined by a set of points in the plane}} ...cern lower bounds on the number of lines ''determined'' by a set of points in the plane. (Any line containing at least two points of point set is said to ...

...s, valuations and quadratic forms | series=CBMS Regional Conference Series in Mathematics | volume=52 | publisher=[[American Mathematical Society]] | yea ...n Lam |title=A first course in noncommutative rings |series=Graduate Texts in Mathematics|volume=131 |edition=2nd |publisher=Springer-Verlag |place=New Y ...

...sher=[[Pearson PLC|Pearson]]|page=119|edition=second}}</ref> ''Metrization theorems'' are [[theorem]]s that give [[sufficient condition]]s for a topological sp ==Metrization theorems== ...

{{Group theory sidebar |Discrete}} ...of a lattice <math display = "inline"> L </math> is the reciprocal of the geometry of <math display = "inline"> L </math>, a perspective which underlies many ...

{{Short description|Branch of differential geometry}} {{General geometry |branches}} ...

...)|intersection]] of [[convex set]]s. It was discovered by [[Eduard Helly]] in 1913,<ref>{{harvtxt|Danzer|Grünbaum|Klee|1963}}.</ref> but not published by We prove the finite version, using [[Radon's theorem]] as in the proof by {{harvtxt|Radon|1921}}. The infinite version then follows by t ...

...e geometry]], '''Tverberg's theorem''', first stated by [[Helge Tverberg]] in 1966,<ref>{{citation ....1112/jlms/s1-41.1.123}}</ref> is the result that sufficiently many points in [[Euclidean space]] can be [[partition of a set|partitioned]] into [[subset ...

{{Short description|Modern reformulation of the calculus in terms of infinitesimals}} ...crete]] entities. As a theory, it is a subset of [[synthetic differential geometry]]. ...

...the theme of ''classical'' discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some (most ...n be described as the study of inevitable irregularities of distributions, in [[Measure theory|measure-theoretic]] and [[Combinatorics|combinatorial]] se ...

...the convex hull of a set P in Rd, is the convex combination of d+1 points in P}} ...from <math>P</math> without changing the membership of ''<math>x</math>'' in the convex hull. ...

In [[mathematics]], a '''prime geodesic''' on a [[hyperbolic geometry|hyperbolic]] [[Surface (topology)|surface]] is a '''primitive''' [[closed g ...section presents some facts from [[hyperbolic geometry]] that are helpful in understanding prime geodesics. ...

...ery [[Singleton (mathematics)|singleton subset]] is an [[open set]] in the discrete topology. ...{visible anchor|discrete topological space}}''' if it is equipped with its discrete topology; ...

...n]] of the field <math>K=k(x_1,\dots,x_n)</math> of [[rational functions]] in <math>n</math> variables over <math>k</math>. As an example, in the [[polynomial ring]] <math>k[x,y]</math> consider the [[ideal (ring theo ...