Compact polyhedral pair: Difference between revisions
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==Definition== | ==Definition== | ||
A pair <math(X,A)</math> where <math>X</math> is a [[topological space]] and <math>A</math> is a subspace, is termed a '''compact polyhedral pair''' if there is a (finite) simplicial complex <math>K</math> with a subcomplex <math>L</math>, and a [[triangulation]] (viz, a homeomorphism) <math>h:|K| \to X</math> such that <math>h(|L|) = A</math>. | A pair <math>(X,A)</math> where <math>X</math> is a [[topological space]] and <math>A</math> is a subspace, is termed a '''compact polyhedral pair''' if there is a (finite) simplicial complex <math>K</math> with a subcomplex <math>L</math>, and a [[triangulation]] (viz, a homeomorphism) <math>h:|K| \to X</math> such that <math>h(|L|) = A</math>. | ||
Complex polyhedlra pairs are important because we can do homology theory for these instead of just for polyhedra. | Complex polyhedlra pairs are important because we can do homology theory for these instead of just for polyhedra. | ||
Revision as of 01:51, 22 May 2007
Template:Topospace-subspace property
Definition
A pair where is a topological space and is a subspace, is termed a compact polyhedral pair if there is a (finite) simplicial complex with a subcomplex , and a triangulation (viz, a homeomorphism) such that .
Complex polyhedlra pairs are important because we can do homology theory for these instead of just for polyhedra.