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Introduce T_0 and T_1 spaces and prove T_1 -> T0. #438
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Actually I used setC1E since it makes the other proof cleaner. |
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Thank you for your contribution!
For T_0 and T_1, we should maybe go with full names like we did for
It can be a one-liner, I am not sure about the naming either, I would propose to name it on the model of |
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FYI
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- `setC_subset_set1C` rename to `mem_setC_subset` on the model of the lemma `disjoints_subset` - `setC1E` rather than `set1CE` with equality the other way around - rename `T_0` and `T_1` to `kolmogorov` and `accessible` on the model of `hausdorff` - update changelog and documentation
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Double-checked and comments from the last meeting applied. Ready to merge.
This PR adds T0 and T1 spaces definitions, proof that singletons in T1 space are closed, and that T1 -> T0.
I introduced 2 lemmas in classical_sets to make easy to work with [set~ x] : setC_set1C and setC_subset_set1C. I'm not really sure about the naming convention:
For "T_1_singleton_closed" I have an extra "have xNeqY:" step, I don't know if it can't be more elegantly derived using the setC_set1C lemma.