Is it possible to map empty space?

I once heard someone say their birth certificate just said born 4 miles from the post office in nowhere.

Map, I think yes.
Purchase, I think not (or maybe from a shady company that makes you believe you can buy a section, but really only take your money and give you a piece of worthless paper which says you now one part 6,733,910 V45.7)

You would need to specify a landmark, the sun being the obvious choice, making use of the fact that all the planets rotate in the same plane. Everything is in motion, including the entire galaxy, which is on a collision course with Andromeda.. Link

If you have enough black paint then yes.

Yes, as long as you have a starting point.

Well, it’s a good starting point to realize that property ownership is an imaginary concept, backed by social agreement and/or less social laws and contracts, which at some fundamental level are imperialistic violence.

Who are you going to pay to buy some certificate of ownership? Who would have the authority to sell it? What would it even mean? Should Jeff Bezos be able to buy a shell-shaped area of space around the Earth, and then charge a few for anyone who sends something through that space?

What frame of reference would one use to chart such ownership? Relative to the sun, I suppose, probably with a directional axis toward the center of the galaxy, or some distant star?

It reminds me of European empires signing agreements with each other to divide up parts of the Earth that they hadn’t even explored yet.

The idea of rich people using their excess money to claim sectors of space seems like a very nasty form of egoic greed to me.

On the other hand, perhaps a license or fee for using space might be worthwhile, if we had some benevolent and worthwhile and not corrupt agency to receive it. Because as corporations and egomaniac billionaires continue to send more and more crap into space, it has serious impacts in terms of resources used, environmental impacts, risks, and littering near-Earth space with obstacles and debris.

Check out http://www.stuffin.space/ !

Map what? It’s empty space. And anything and everything that might be there is moving around.

From Wikipedia:
https://en.wikipedia.org/wiki/Galactic_quadrant
“The delineation of the galactic quadrants is based upon the galactic coordinate system, which places the Sun as the pole of the mapping system. The Sun is used instead of the Galactic Center for practical reasons since all astronomical observations (by humans) to date have been based on Earth or within the Solar System.”
“Galactic quadrants within Star Trek are based around a meridian that runs from the center of the Galaxy through Earth’s Solar System, which is not unlike the system used by astronomers. However, rather than have the perpendicular axis run through the Sun, as is done in astronomy, the Star Trek version runs the axis through the galactic center. In that sense, the Star Trek quadrant system is less geocentric as a cartographical system than the standard. Also, rather than use ordinals, Star Trek designates them by the Greek letters Alpha, Beta, Gamma, and Delta.
The Canadian Galactic Plane Survey (CGPS) created a radio map of the Galaxy based on Star Trek’s quadrants…”