Mark each of the following true or false. 

___ a. Homeomorphic simplicial complexes have isomorphic homology groups. 

___ b. If two simplicial complexes have isomorphic homology groups, then the spaces are homeomorphic. 

___ c. sⁿ is homeomorphic to Eⁿ. 

___ d. H_n(X) is trivial for n > 0 if X is a connected space with a finite triangulation. 

___ e. H_n(X) is trivial for n > 0 if X is a contractible space with a finite triangulation. 

___ f. H_n(Sⁿ) = 0 for n > 0. 

___ g. H_n(Eⁿ) = 0 for n > 0. 

___ h. A torus is homeomorphic to S².

___ i. A torus is homeomorphic to E².

___ j. A torus is homeomorphic to a sphere with a handle on it (see Fig. 42.17).