feat(Topology/SpectralSpace/ConnectedComponent): prove T2Space ConnectedComponents#23
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chrisflav merged 4 commits intochrisflav:masterfrom Mar 16, 2026
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…tedComponents Prove `t2Space_connectedComponent`: the connected components space of a quasi-separated prespectral compact space is Hausdorff (Stacks 0906). Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
chrisflav
commented
Mar 16, 2026
- Revert unrelated change at line 97 - Remove unnecessary docstring - Use `rw [t2Space_iff]` without extra parentheses - Extract `hsat` inline into standalone lemma `IsClopen.connectedComponents_image_isClopen` Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
- Replace `by simp [isClopen_univ]` with explicit `isClopen_univ, Set.mem_univ _` - Add missing `exact hU` after rewrites in `connectedComponents_image_isClopen` Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
chrisflav
commented
Mar 16, 2026
- Revert unrelated change at line 97 back to `by simp [isClopen_univ]` - Move `IsClopen.connectedComponents_image_isClopen` to `TotallyDisconnected.lean` (earlier in the import hierarchy) Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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Prove
t2Space_connectedComponent: the connected components space of a quasi-separated prespectral compact space is Hausdorff (Stacks 0906).