General Topology II - National Open University of Nigeria
General Topology II - National Open University of Nigeria

Geometry - Singapore American School
Geometry - Singapore American School

C -algebras over topological spaces: the bootstrap class
C -algebras over topological spaces: the bootstrap class

Project Gutenberg`s The Foundations of Geometry, by David Hilbert
Project Gutenberg`s The Foundations of Geometry, by David Hilbert

Richmond Public Schools
Richmond Public Schools

COMBINATORIAL HOMOTOPY. I 1. Introduction. This is the first of a
COMBINATORIAL HOMOTOPY. I 1. Introduction. This is the first of a

Paracompactness with respect to an ideal
Paracompactness with respect to an ideal

Covariance algebra of a partial dynamical system - MATH Mail
Covariance algebra of a partial dynamical system - MATH Mail

On Noetherian Spaces - LSV
On Noetherian Spaces - LSV

Geometry - Hickman County Schools
Geometry - Hickman County Schools

Grade 6 – Number and Operation
Grade 6 – Number and Operation

1 Comparing cartesian closed categories of (core) compactly
1 Comparing cartesian closed categories of (core) compactly

... spaces, it is hardly ever the case that the exponential [X ⇒ Y ] is again exponentiable. In fact, the full subcategory of exponentiable spaces also fails to be cartesian closed. Nonetheless, Top is known to possess several cartesian closed full subcategories, including: (i) Compactly generated Hausd ...
(core) compactly generated spaces
(core) compactly generated spaces

RATIONAL HOMOTOPY THEORY Contents 1. Introduction 1 2
RATIONAL HOMOTOPY THEORY Contents 1. Introduction 1 2

Geometry EOC Assessment Test Item Specifications, Version 2
Geometry EOC Assessment Test Item Specifications, Version 2

... 6. For the Algebra 1 End-of-Course Assessment, a four-function calculator will be allowed. For the Geometry End-of-Course Assessment, a scientific calculator will be allowed. 7. Test items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; howeve ...
Foundations of Geometry
Foundations of Geometry

Quadrilaterals - Elmwood Park Memorial High School
Quadrilaterals - Elmwood Park Memorial High School

Unit Review
Unit Review

Introduction to General Topology
Introduction to General Topology

Analogues of Cayley graphs for topological groups
Analogues of Cayley graphs for topological groups

9 Neutral Triangle Geometry
9 Neutral Triangle Geometry

Integrated Geometry - Calendar of Lessons
Integrated Geometry - Calendar of Lessons

On superpositionally measurable semi Carath eodory multifunctions
On superpositionally measurable semi Carath eodory multifunctions

1. The Baire category theorem
1. The Baire category theorem

Notes - WVU Math Department
Notes - WVU Math Department

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.