TYPO3 Core

Hi,
when I install typo3 not into the root directory of the webserver but into a subdirectory, everything is fine except that the link in the upper left corner in the backend (in the top bar where is also the logout and the search term on the right side)
points to the root of the webserver (http://localhost/) but I would prefer it would point to the subdirectory (http://localhost/subdirectory) where typo3 is installed.

When installing Bootstrap package there is a new buttton on the very left which points also to the webroot (http://localhost/) instaed of the (http://localhost/subdirectory)

Best regards
Eckard.