Compact polyhedral pair: Difference between revisions

Revision as of 01:51, 22 May 2007

Definition

A pair $(X, A)$ where $X$ is a topological space and $A$ is a subspace, is termed a compact polyhedral pair if there is a (finite) simplicial complex $K$ with a subcomplex $L$ , and a triangulation (viz, a homeomorphism) $h : | K | \to X$ such that $h (| L |) = A$ .

Complex polyhedlra pairs are important because we can do homology theory for these instead of just for polyhedra.

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 ==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.