Take the 2-minute tour ×
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.

Are there any topological spaces $X$ with subspaces $A$ such that $H_n(X,A)$ is not isomorphic to $H_n(X/A)$?

I've been trying some familiar spaces, but everything seems to be me an isomorphism via the quotient map. Does anyone know of any examples?

share|improve this question
Hatcher gives the following as an excercise in section 2.1 of his Algebraic topology book. Let $X = [0,1]$ and $A = \{\frac{1}{n}\} \cup \{0\}$. Then $H_1(X,A)$ is not isomorphic to $H_1(X/A)$. –  Jason DeVito Nov 19 '12 at 17:59

Your Answer


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

Browse other questions tagged or ask your own question.