Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Introduce T_0 and T_1 spaces and prove T_1 -> T0. #438

Merged
merged 4 commits into from
Jan 6, 2022

Conversation

vlj
Copy link
Contributor

@vlj vlj commented Sep 26, 2021

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:

  • setC_set1C isn't technically an elimination so it can't be named set1C, but it's very close... I wonder if it's not better to have a Lemma proving "[y | y != x] = [set~ x]".
  • setC_subset_set1C is involving a subset of set1C, but I don't know how to phrase it correctly. I'm also not sure my proof is optimal.
    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.

@vlj vlj force-pushed the T_X_spaces branch 2 times, most recently from 4018323 to 874d1c4 Compare September 26, 2021 21:43
@vlj
Copy link
Contributor Author

vlj commented Sep 26, 2021

Actually I used setC1E since it makes the other proof cleaner.

@affeldt-aist
Copy link
Member

This PR adds T0 and T1 spaces definitions, proof that singletons in T1 space are closed, and that T1 -> T0.

Thank you for your contribution!

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_0 and T_1, we should maybe go with full names like we did for hausdorff, otherwise it looks too much
like code identifier.

* setC_subset_set1C is involving a subset of set1C, but I don't know how to phrase it correctly.

I'm also not sure my proof is optimal.

It can be a one-liner, I am not sure about the naming either, I would propose to name it on the model of
disjoints_subset because it looks like a special case.

@affeldt-aist affeldt-aist self-assigned this Oct 13, 2021
@affeldt-aist affeldt-aist added the enhancement ✨ This issue/PR is about adding new features enhancing the library label Oct 13, 2021
@affeldt-aist affeldt-aist added this to the 0.3.12 milestone Oct 13, 2021
@affeldt-aist affeldt-aist force-pushed the T_X_spaces branch 2 times, most recently from 55bd581 to 03f5954 Compare December 3, 2021 07:18
@CohenCyril
Copy link
Member

CohenCyril commented Dec 8, 2021

FYI

  • removed useless setC1E (it is convertible and inE yields the same result)
  • removed mem_setC_subset which was a duplicate of setC_subset_set1C
  • generalized and renamed the latter to subsetC1
  • removed all uses of -in_setE

vlj and others added 4 commits December 29, 2021 18:07
- `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
- removed useless `setC1E` (it is convertible and `inE` yields the same result)
- removed `mem_setC_subset` which was a duplicate of `setC_subset_set1C`
- generalized and renamed the latter to `subsetC1`
- removed all uses of `-in_setE`
- following 2021-12-16 meeting
Copy link
Member

@affeldt-aist affeldt-aist left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Double-checked and comments from the last meeting applied. Ready to merge.

@CohenCyril CohenCyril merged commit bed1521 into math-comp:master Jan 6, 2022
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
enhancement ✨ This issue/PR is about adding new features enhancing the library
Projects
None yet
Development

Successfully merging this pull request may close these issues.

3 participants