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...[CW complex]] up to isomorphism are in bijection with [[homotopy]] classes of its [[Continuous function|continuous]] maps into <math>\operatorname{BSU}(n There is a canonical inclusion of complex oriented Grassmannians given by <math>\widetilde\operatorname{Gr}_n ...

In [[mathematics]], a '''Busemann ''G''-space''' is a type of [[metric space]] first described by [[Herbert Busemann]] in 1942. # every <math>d</math>-bounded set of infinite cardinality possesses [[accumulation point]]s ...

...tract [[algebraic geometry]] and to describe some basic uses of projective spaces. == Homogeneous polynomial ideals== ...

...ematical]] fields of [[Lie theory]] and [[algebraic topology]], the notion of '''Cartan pair''' is a technical condition on the relationship between a [[ is isomorphic to the tensor product of the characteristic subalgebra ...

...[CW complex]] up to isomorphism are in bijection with [[homotopy]] classes of its [[Continuous function|continuous]] maps into <math>\operatorname{BSO}(n There is a canonical inclusion of real oriented Grassmannians given by <math>\widetilde\operatorname{Gr}_n(\m ...

For example, the nearly Kähler six-sphere <math>S^6</math> is an example of a nearly Kähler manifold that is not Kähler.<ref> |title=Handbook of Differential Geometry| volume =II |isbn =978-0-444-82240-6 ...

...on <math>\mathbb{Z}</math>, and the '''Golomb topology''' and the '''Kirch topology''' on <math>\mathbb{Z}_{>0}</math>. Precise definitions are given below. ...ese topologies also have interesting [[Separation axiom|separation]] and [[Homogeneous space|homogeneity]] properties. ...

...e [[Taylor series]] of a [[smooth function]], hence the term "''calculus'' of functors". Many objects of central interest in algebraic topology can be seen as functors, which are difficult to analyze directly, so the id ...

.... This notion is often used with ''G'' being a [[Lie group]] and ''X'' a [[homogeneous space]] for ''G''. Foundational examples are [[hyperbolic manifold]]s and [ ...old]] and <math>G</math> be a subgroup of the group of [[diffeomorphism]]s of <math>X</math> which act analytically in the following sense: ...

...|first=Vladimir |title=DG coalgebras as formal stacks|journal = [[Journal of Pure and Applied Algebra]] | volume= 162| year=2001|issue =2–3 | pages=209– ...space <math>L = \bigoplus L_i</math> over a [[field (mathematics)|field]] of [[characteristic (algebra)|characteristic]] zero together with a bilinear m ...

...harmonic functions on the domain. Harmonic morphisms form a special class of [[harmonic map]]s, namely those that are horizontally (weakly) conformal.<r ...<math>M</math> and <math>y</math> on <math>N</math>, the '''harmonicity''' of <math>\phi</math> is expressed by the [[non-linear]] system ...

...er the ring of polynomials invariant under the [[finite reflection group]] of a [[root system]]. ...{harvtxt|Demazure|1973}} as a tool to understand the [[Schubert calculus]] of the flag manifold. The Kostant polynomials are related to the [[Schubert po ...

...e_1_Display_Small.png|thumb|The configuration space of all unordered pairs of points on the circle is the [[Möbius strip]].]] ...R. Wilson, at Harvard University.JPG|upright|thumb|The configuration space of 3 not necessarily distinct points on the circle <math>T^3/S_3,</math> is th ...

...e translated in terms of considering solutions in some convenient function spaces. ...hp?title=Differential_equation,_abstract&oldid=14482 |website=Encyclopedia of Mathematics}}</ref> ...

{{About|dual pairs of vector spaces|dual pairs in representation theory|Reductive dual pair|the recycling syste ...ld]] <math>\mathbb{K}</math> is a triple <math>(X, Y, b)</math> consisting of two [[vector space]]s, <math>X</math> and <math>Y</math>, over <math>\mathb ...

{{Short description|Subspace defined by a polynomial of degree 2 over a field}} [[File:Hyperboloide1.png|thumb|right|The two families of lines on a smooth (split) quadric surface]] ...

...e|rational spaces]] whose rational homotopy type is a "formal consequence" of their [[cohomology ring]] with rational coefficients. Informally, this mea ...ges=245-274 |doi=10.1007/BF01389853}}</ref> to classify the homotopy types of [[Kähler manifolds]]. ...

...^''X''''H''}} is an analytic bijection onto an open neighborhood of {{math|''H''}} in {{math|''G''}}}}{{sfn|Hall|2015|loc=For linear groups, Ha ...inspired by [[John von Neumann]]'s 1929 proof of a special case for groups of [[linear map|linear transformations]].{{sfn|von Neumann|1929}}{{sfn|Bochner ...

...of points and the intersection point of two lines is a continuous function of these lines. ...of linear topological geometries is given in Chapter 23 of the ''Handbook of incidence geometry''.<ref>{{harvnb|Grundhöfer|Löwen|1995}}</ref> The most e ...

...ial function]]s that are defined locally by [[rational fraction]]s instead of polynomials. ...gebraic varieties is precisely a morphism of the underlying locally ringed spaces. ...