Poincare Conjecture Proof - Gauge-institute.org
Poincare Conjecture Proof - Gauge-institute.org
Poincare Conjecture Proof - Gauge-institute.org
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<strong>Poincare</strong> <strong>Conjecture</strong> <strong>Proof</strong>H. Vic Dannon24.4 Each Σθis Hausdorff<strong>Proof</strong>: Every subspace of Hausdorff is Hausdorff. 24.5 Each Σ is a 2-manifold with the topology Tθ2<strong>Proof</strong>: Each point x ∈Σ , has a 2-dimensional open neighborhood2 3x x-( θ)θU = U ∩ the angle hyperplane , homeomorphic to a 2-dimensional disk D 2 B 3( the θ-angle hyperplane )x= ∩ .xθ4.6EachΣ2θis Compact2<strong>Proof</strong>: Σθis compact, as a subset of the compact3Σ .24.7 Each Σθis Connected2<strong>Proof</strong>: If Σθis disconnected, then3Σ is disconnected.24.8 Each Σθhas a Closed Finite Triangulation2<strong>Proof</strong>: Σθinherits a finite triangulation from3Σ .2Each side of a triangle in the induced triangulation on Σθ, is onthe face of some tetrahedron from the triangulation of3Σ .10
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