If you connect jQuery 3.2.1, jQuery-UI 1.12.1 in the project and then add Bootstrap 3.3.7, the button for closing the window breaks (it works, but is not displayed correctly):

https://jsfiddle.net/3wfuogvq/

$('<div id="myDlg" title="jQuery 3 + Bootstrap">jQuery ui close button is not shown but it works properly</div>').dialog(); 

If you swap UI and Bootstrap, then the button is displayed normally.
Perhaps there are some more conflicts and incompatibilities - until I come across.

Who worked with these versions of libraries, please tell me how to be friends with them correctly?

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