Given a countably paracompact normal space S with a closed subspace S^1 and a finite derected graph G with a subgraph SG^1, there are bijections from the sets of homotopy classes Q(S,G) and Q(S,S^1;G,G^1) to the sets of o*-homotopy classes Q^\ast(S,G) and Q^\ast(S,S^1;G,G^1) respectively (see 3).Here we prove,by some examples,that certain conditions on S weaker than the ones required in (3) are not sufficent to prove the results given above.

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