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General Topology – Exercise 7 from Munkre's book, page 240

To let $ X $ be a discreet room; consider that $ beta (X) $,

a) Show that if $ A subset X $, then $ overline {A} $ and $ overline {X-A} $ Disjoint are where the closures are received $ beta (X) $,

b) Show that if $ U $ is open in $ beta (X) $, then $ overline {U} $is open in $ beta (X) $,

c) Show that $ beta (X) $ is completely separate.

This is a problem 7 (page 240) from Munkre's book.

I have not yet tried to solve this problem because I can not understand why $ beta (X) $ exists in this case.
He defined $ beta (X) $ This is a Stone-Cech compactification only for fully regular (Tychonoff) rooms. Why should discrete space be Tychonoff space?

That's easy to see $ X $ is Hausdorff room. I can not say more about that.

Can someone please explain my question to me?

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Composer – Strange problems with Drupal 8.7.7 and Drupal / Jsonapi 2.4.0

I'm sharing a release branch with a development team and I'm the only one who has this problem locally (see below).

$ git reset --hard origin/2019-Oct-R2
HEAD is now at 8e5cec59b1 WWW-1599 update spoke service definition and update jsonapi module
$ git status
On branch 2019-Oct-R2
Your branch is up to date with 'origin/2019-Oct-R2'.

nothing to commit, working tree clean

At this time, I'm on the latest release branch and have no tracked or un-tracked files (just like my colleagues). Then I try the following:

$ composer update nothing
Gathering patches for root package.
> DrupalProjectcomposerScriptHandler::checkComposerVersion
Loading composer repositories with package information
Updating dependencies (including require-dev)
Your requirements could not be resolved to an installable set of packages.

  Problem 1
    - Conclusion: remove drupal/core 8.7.7
    - Conclusion: don't install drupal/core 8.7.7
    - don't install drupal/core 8.7.7|remove drupal/jsonapi 2.4.0
    - don't install drupal/jsonapi 2.4.0|don't install drupal/core 8.7.7
    - don't install drupal/jsonapi 2.4.0|don't install drupal/core 8.7.7
    - Installation request for drupal/core 8.7.7 -> satisfiable by drupal/core(8.7.7).
    - Installation request for drupal/jsonapi (locked at 2.4.0, required as ^2.4) -> satisfiable by drupal/jsonapi(2.4.0).

Can someone interpret this error message for me?