Hello,
I would like to create an application in Unity with OpenStreetMap data working offline.
How could i “donwload” the specific map for such use?
Best
adrian@distudios.pl
With OpenStreetMap, generally speaking you don’t download a map, you download the data that was used to create that map.
OpenStreetMap is big (over 70GB compressed) so it’s extremely unlikely that you’ll want to download absolutely everything. You might just want certain types of data (buildings but not the opening times of pharmacies, for example) or data in a certain area.
You’ll need to decide what data is important to you and how you want to store it, and then extract only the data you want from OSM and convert it into that format. There are many, many different ways of doing that - which is best really depends on what it is that you are trying to do.
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Downloading data - OpenStreetMap Wiki may help
note that you may need to convert data into format usable by your tools
Try this: HOT Export Tool
I have downloaded small stretches of map in the osm.pbf format to edit with JOSM for my own use.
Edit: I don’t know Unity but you can download in several formats.
On the site I linked above you can specify what you want. Since I only downloaded small stretches I didn’t bother to look at that and selected everything. Last download was 18 kB 
You probably could use Qgis to read the OSM data and export it into some format Unity can understand, but with the current scandal around Unity, I’d not recommend starting a project with it.