Determine the structure of the homology group H_n(X), n >= 0, if X is
(a) the set of rational numbers with their usual topology;
(b) a countable, discrete set.
Homology group - (See attached file for full problem description)
---
Determine the structure of the homology group Hn(X), n 0, if X is
(a) the set of rational numbers with their usual topology;
(b) a c ...
Continuous Maps, Homomorphisms and Cyclic Groups - Let f: S^n --> S^n be a continuous map.
Consider the induced homomorphism f*: H~_n (S^n) --> H~_n (S^n), where
H~_n is a reduced homology group. Then from the fact that H~_n (S^n) is an infinite
cy ...
The Exact Homology Sequence (Exact Sequence of Triples) - Problem:
Let X = X_1 / X_2, and A = X_1 / X_2. Using the exact sequence of triples, show that if the inclusion (X_1, A) --> (X, X_2) induces an isomorphism on homology, then the same holds for ...