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...efer to two different formulae in [[differential geometry]] or [[algebraic topology]]. ==Cartan formula in differential geometry== ...

In [[algebraic topology]] and [[algebraic geometry]], '''Leray's theorem''' (so named after [[Jean Leray]]) relates a ...}) = 0</math> for all <math>i \ge 1</math> and all <math> U_1, \dots, U_p \in \mathcal{U})</math>, then ...

[[:Category:Algebraic geometry|Algebraic&nbsp;geometry]] | [[:Category:Topology|Topology]] | ...

Several theorems proved by the French [[mathematician]] [[Claude Chevalley]] bear his name. * [[Chevalley–Shephard–Todd theorem]] in [[invariant theory]] of [[finite group]]s. ...

...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]]. ...

...y)|twisting]], crumpling and bending, but not tearing or [[Quotient space (topology)|gluing]]. ...line (geometry)|line]] and a [[surface (mathematics)|surface]]; [[compact (topology)|compactness]], which allows distinguishing between a line and a circle; [[ ...

This is a '''list of [[general topology]] topics'''. **[[Closure (topology)|Closure]] ...

...em''' is a result in the [[mathematics|mathematical]] field of [[algebraic topology]]. It is named for [[Leopold Vietoris]] and [[Edward G. Begle]]. The statem ...^{-1}(y)) = 0,</math> for all <math>0\leq r\leq n-1</math> and all <math>y\in Y</math>, ...

...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== ...

...[[acyclic sheaf|acyclic]] [[injective resolution|resolution]] of the sheaf in question. ...q</math>-th [[sheaf cohomology]] group of <math>X</math> with coefficients in <math>\mathcal F.</math> ...

{{Short description|Theorem in algebraic topology}} In [[algebraic topology]], a branch of [[mathematics]], the '''excision theorem''' is a theorem abo ...

{{short description|Number of connected components an algebraic curve can have}} ...s of the degree of the curve. For any algebraic curve of degree {{mvar|m}} in the real [[projective plane]], the number of components {{mvar|c}} is bound ...

...lly simply connected if there is a lower bound on the sizes of the “holes” in ''X''. This condition is necessary for most of the theory of covering space ...The neighborhood ''U'' need not be [[simply connected]]: though every loop in ''U'' must be contractible within ''X'', the contraction is not required to ...

{{short description|Type of algebraic variety}} ...ety {{mvar|Y}} the [[Product (category theory)|projection]] [[Regular map (algebraic geometry)|morphism]] ...

...mathematics]], the '''Hurewicz theorem''' is a basic result of [[algebraic topology]], connecting [[homotopy theory]] with [[homology theory]] via a map known ==Statement of the theorems== ...

...mplicial approximation theorem''' is a foundational result for [[algebraic topology]], guaranteeing that [[continuous mapping]]s can be (by a slight deformatio ...ome other areas. This initiated, one could say, the era of [[combinatorial topology]]. ...

{{short description|Theorem stating that smooth algebraic curve has minimum genus its homology class}} ...ex projective plane]], of degree <math>d</math>, has [[Genus_(mathematics)#Topology|genus]] given by the [[genus–degree formula]] ...

{{About|topological notion|related algebraic notion|Mapping cylinder (homological algebra)}} ...ogical space]]s <math>X</math> and <math>Y</math> is the [[Quotient space (topology)|quotient]] ...

...o [[Function of several complex variables|several complex variables]], and in the general development of [[sheaf cohomology]]. Theorem B is stated in cohomological terms (a formulation that Cartan ([[#CITEREFCartan1953|1953]] ...

...nstructing numerical [[Invariant (mathematics)|invariants]] related to the topology of a smooth [[Deformation (mathematics)|deformation]] of the singular space ...Dimca| url=https://www.worldcat.org/oclc/852790417|title=Singularities and Topology of Hypersurfaces|date=1992|publisher=[[Springer Science+Business Media|Spri ...