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Mathematics - Geometry
Mathematics - Geometry

On the works of Euler and his followers on spherical geometry
On the works of Euler and his followers on spherical geometry

Metric geometry of locally compact groups
Metric geometry of locally compact groups

... setting, we distinguish four classes, each class properly containing the next one: (all) all discrete groups; (ct) countable groups; (fg) finitely generated groups; (fp) finitely presented groups. This will serve as a guideline below, in the more general setting of locally compact groups. Every group ...
General Topology
General Topology

Ideal amenability of Banach algebras on locally compact groups
Ideal amenability of Banach algebras on locally compact groups

Dynamical characterization of C
Dynamical characterization of C

Metrization Theorem
Metrization Theorem

6.5 Trapezoids and Kites
6.5 Trapezoids and Kites

Sheaf theory - Department of Mathematics
Sheaf theory - Department of Mathematics

Synthetic topology - School of Computer Science, University of
Synthetic topology - School of Computer Science, University of

Varieties of two-dimensional cylindric algebras
Varieties of two-dimensional cylindric algebras

on if generalized* minimal open set
on if generalized* minimal open set

topology - DDE, MDU, Rohtak
topology - DDE, MDU, Rohtak

Georgia Geometry Unit 2 - Milwaukee Public Schools
Georgia Geometry Unit 2 - Milwaukee Public Schools

Unit 2 - Georgia Standards
Unit 2 - Georgia Standards

topologies for function spaces
topologies for function spaces

Topologies on function spaces and hyperspaces
Topologies on function spaces and hyperspaces

For printing
For printing

... to (1.4). We call the former class of topologies proper, and the latter admissible. The following questions about this class of topologies in Zγ are considered in this paper: What are the relations (in the sense of the conventional partial ordering of topologies) of the proper topologies to the admi ...
The Brauer group of a locally compact groupoid - MUSE
The Brauer group of a locally compact groupoid - MUSE

... equivalence classes of such representations will be denoted R(G). With respect to the process of forming tensor products, it is not difficult to see that R(G) becomes a semigroup with identity in a natural way. The problem is to describe this semigroup. Owing to Wigner’s theorem [57] that all -auto ...
Scott Topology and its Relation to the Alexandroff Topology
Scott Topology and its Relation to the Alexandroff Topology

my solutions.
my solutions.

... Uα,1 ∩ · · · ∩ Uα,mα ∩ Uβ,1 ∩ · · · ∩ Uβ,nβ , (α,β)∈A×B ...
NONLINEAR ANALYSIS MATHEMATICAL ECONOMICS
NONLINEAR ANALYSIS MATHEMATICAL ECONOMICS

Second duals of measure algebras
Second duals of measure algebras

... The above definition was first given in [17, Definition 12.4]; care is required because this term has been used in a slightly different sense elsewhere. Let S be a semigroup, and let ` 1 (S) be the corresponding semigroup algebra. In [17], it is shown that, for an interesting class of semigroups str ...
hohology of cell complexes george e. cooke and ross l. finney
hohology of cell complexes george e. cooke and ross l. finney

... The correspondence here between geometry and algebra is often cru.de. Topologically distinct spaces may be made to correspond to the same a l ge ­ For example, a disc and a point have the same homology ...
separability of metric spaces - American Mathematical Society
separability of metric spaces - American Mathematical Society

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Geometrization conjecture

In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply-connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic).In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston (1982), and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print.Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery.There are now several different manuscripts (see below) with details of the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.
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