bigcup_ointsub disjoint

[affeldt-aist]

Motivation for this change

This is a definition of the sequence of non-overlapping open intervals that covers an open interval of real numbers. It is used in particular to define contiguous intervals.

@IshiguroYoshihiro can you double-check?

Checklist

• added corresponding entries in CHANGELOG_UNRELEASED.md

• added corresponding documentation in the headers

Reference: How to document

Merge policy

As a rule of thumb:

• PRs with several commits that make sense individually and that
  all compile are preferentially merged into master.
• PRs with disorganized commits are very likely to be squash-rebased.

Reminder to reviewers

• Read this Checklist
• Put a milestone if possible
• Check labels

[affeldt-aist]

@IshiguroYoshihiro can you double-check?

ping

[t6s]

if I understand correctly, this PR is about the fact that open intervals form an open basis of the real line, but by quickly reading , I could not notice in the changes anything about basis. am I missing something?

[affeldt-aist]

if I understand correctly, this PR is about the fact that open intervals form an open basis of the real line

this is just the proof that an open set can be covered by open intervals, nothing was attempted about basis

[t6s]

I have understood that this is not merely about the basis, but what matters here is the disjointness.

[IshiguroYoshihiro]

@IshiguroYoshihiro can you double-check?

It looks good for me.

[t6s]

I have quickly checked the statements, and they do not look bad.

[affeldt-aist]

Thanks for the double-check!