User:Netnubie/sandbox

Compression Lemma
Let $$(X,A)$$ be a CW pair and let $$(Y,B)$$ be any pair with $$B\neq \emptyset$$. For each $$n$$ such that $$X-A$$ has cells of dimension $$n$$, assume that $$\Pi_n(Y,B,y_0) = 0$$ for all $$y_0\in B$$. Then every map $$f:(X,A) \rightarrow (Y,B).$$ then every map $$f:(X,A)\rightarrow (Y,B)$$ is homotopic rel $$A$$ to a map $$g:X\rightarrow B$$.