Compact polyhedral pair: Difference between revisions

Latest revision as of 19:41, 11 May 2008

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

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