mathboy
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I know that a product of Hausdorff spaces is Hausdorff. Is the converse also true? That is, if A_1 x A_2 x A_3 x... is Hausdorff, then is each A_i Hausdorff?
PxH is empty if P is empty because if f belonged to PxH, then f(1) would belong to P and f(2) would belong to H. But f(1) cannot belong to P because P is empty. So there is no such f.Singularity said:If say, P is the empty set with the discrete topology and H is another hausdorff space,
will PxH be homeomorphic to H?
Singularity said:Can a function "belong" to a space? I have never heard of this. Also, your argument only has one component, when it seems like it should have two. Am I missing something fundamental here?
Thanks :)