Polyhedron: Difference between revisions
No edit summary |
|||
| Line 10: | Line 10: | ||
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=== | |||
* [[Manifold]] | |||
* [[Pseudomanifold]] | |||
===Weaker properties=== | |||
* [[CW-space]] | |||
Revision as of 00:30, 27 October 2007
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 .