[Merged by Bors] - feat(counterexamples/sorgenfrey_line): new file #14820
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counterexamples/sorgenfrey_line.lean
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| @[derive [conditionally_complete_linear_order, linear_ordered_field, archimedean]] | ||
| def sorgenfrey_line : Type := ℝ | ||
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| notation `ℝₗ` := sorgenfrey_line |
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local notation? Maybe someone will need to import this file someday.
counterexamples/sorgenfrey_line.lean
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| (Ici_prod_eq x).symm ▸ (is_clopen_Ici _).prod (is_clopen_Ici _) | ||
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| lemma is_closed_of_subset_antidiagonal {s : set (ℝₗ × ℝₗ)} {c : ℝₗ} | ||
| (hs : ∀ x ∈ s, (x : _).1 + x.2 = c) : is_closed s := |
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could you fill in the underscore to help the reader?
| lemma is_clopen_Ici_prod (x : ℝₗ × ℝₗ) : is_clopen (Ici x) := | ||
| (Ici_prod_eq x).symm ▸ (is_clopen_Ici _).prod (is_clopen_Ici _) | ||
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| lemma is_closed_of_subset_antidiagonal {s : set (ℝₗ × ℝₗ)} {c : ℝₗ} |
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can you add a docstring to this lemma, because it is both important and striking?
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Define the Sorgenfrey line and prove that it is a normal topological space but its product with itself is not a normal topological space.
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Define the Sorgenfrey line and prove that it is a normal topological space but its product with itself is not a normal topological space.
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Define the Sorgenfrey line and prove that it is a normal topological space but its product with itself is not a normal topological space.
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Define the Sorgenfrey line and prove that it is a normal topological space but its product with itself is not a normal topological space.
Should it go to
counterexamples/orsrc/topology/instances?