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The one-point compactification of the rationals is a Fréchet-Urysohn space, each of whose compact subsets is closed. In particular, it is compactly generated. It is compact, so paracompact by your definition. But is it is not Hausdorff.
The one-point compactification of the rationals is a Fréchet-Urysohn space, each of whose compact subsets is closed. In particular, it is compactly generated. It is compact, so paracompact by your definition. But is it not Hausdorff.
The one-point compactification of the rationals is a Fréchet-Urysohn space, each of whose compact subsets is closed. In particular, it is compactly generated. It is compact, so paracompact by your definition. But it is not Hausdorff.
The one-point compactification of the rationals is a Fréchet-Urysohn space, each of whose compact subsets is closed. In particular, it is compactly generated. It is compact, so paracompact by your definition. But is it not Hausdorff.