Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This is a screenshot from Hatcher's Algebraic Topology.enter image description here

I can't understand the last sentence. By definition $C_n(X)$ is the free $\mathbb Z$-module generated by all n-simplices. But, why should every singular map go to exactly exactly $A$ or $X-A$ -- what about maps whose images lie in $A$ and a bit outside? And if this were true, why bother with barycentric subdivisions?


share|cite|improve this question

1 Answer 1

up vote 4 down vote accepted

«A simplex whose image is not contained in $A$» is not the same thing as «a simplex whose image is contained in $X-A$».

share|cite|improve this answer
Thanks (bangs head against desk). – Dignaga Nov 16 '11 at 15:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.