ENH: Add set_closed method to IntervalIndex
- [X] closes #21670
- [X] tests added / passed
- [X] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [X] whatsnew entry

# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=h1) Report
> Merging [#21711](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/7cd2679982138e1e7f9f1a759827647e6e521d43?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/21711/graphs/tree.svg?width=650&height=150&src=pr&token=eZ4WkYLtcO)](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #21711      +/-   ##
==========================================
+ Coverage    91.9%   91.91%   +<.01%     
==========================================
  Files         158      158              
  Lines       49690    49695       +5     
==========================================
+ Hits        45670    45675       +5     
  Misses       4020     4020
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.28% <100%> (ø)` | :arrow_up: |
| #single | `41.95% <20%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/21711/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9pbnRlcnZhbC5weQ==) | `93.18% <100%> (+0.05%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=footer). Last update [7cd2679...9428144](https://codecov.io/gh/pandas-dev/pandas/pull/21711?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 lgtm. @jorisvandenbossche @TomAugspurger  FYI - I'll refrain from doing any additional `IntervalIndex` updates after this, so as not to cause conflicts with any `IntervalArray` work (I'm assuming that @TomAugspurger or I will be working on that at some point during the sprint). Sounds good.

Would be nice to knock out IntervalArray during the sprint.