For two open disjoint subsets U and V, I want to show their pre-images are disjoint open subsets of X or not. But I have no idea how to do it.
Any help would be appreciated. Thanks in advance!
2026-03-25 04:59:35.1774414775
Prove or disprove if a quotient map from X to Y with Y Hausdorff, then X is Hausdorff.
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This is not true. Map $\mathbb R$ with the indiscrete topology to any one point set. The one point set is Hausdorff while $\mathbb R$ under the indiscrete topology is not.