Polyhedron: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[topological space]] is termed a '''polyhedron''' if there is a homeomorphism to it from the underlying space of a (finite) [[simplicial complex]]. The simplicial complex, along with the homeomorphism, is termed a [[triangulation]] of the topological space. | A [[topological space]] is termed a '''polyhedron''' if there is a homeomorphism to it from the underlying space (viz, [[geometric realization]]) of a (finite) [[simplicial complex]]. The simplicial complex, along with the homeomorphism, is termed a [[triangulation]] of the topological space. | ||
===Definition with symbols=== | ===Definition with symbols=== | ||
A [[topological space]] <math>X</math> is termed a '''polyhedron''' if there is a (finite) simplicial complex <math>K</math> and a homeomorphism <math>h:|K| \to X</math>. The pair <math>(K,h)</math> is termed a [[triangulation]] of <math>X</math>. | A [[topological space]] <math>X</math> is termed a '''polyhedron''' if there is a (finite) simplicial complex <math>K</math> and a homeomorphism <math>h:|K| \to X</math>. The pair <math>(K,h)</math> is termed a [[triangulation]] of <math>X</math>. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Differentiable manifold]] | |||
===Weaker properties=== | |||
* [[CW-space]] | |||
Latest revision as of 06:40, 22 June 2016
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
Symbol-free definition
A topological space is termed a polyhedron if there is a homeomorphism to it from the underlying space (viz, geometric realization) of a (finite) simplicial complex. The simplicial complex, along with the homeomorphism, is termed a triangulation of the topological space.
Definition with symbols
A topological space is termed a polyhedron if there is a (finite) simplicial complex and a homeomorphism . The pair is termed a triangulation of .