mcgeehe: No, this game dose not require an internet connection. You can install and play completely offline. Seeing how the game uses procedural generation, nothing is stored on the hard drive or a server, it is generated by the computer each time you visit a system/planet, and is
"thrown away" when you leave. It's covered on the page.
https://blog.eu.playstation.com/2015/08/03/41-amazing-things-you-might-not-know-about-no-mans-sky/
Edit: See topic #3 on that page about procedural generation and offline play.
I thought one of the more recent interviews stated that it stores things you do locally? Yes, the planet and anything not in sight is discarded (i.e. it doesn't actually save all the planet's info) but your actions were supposed to persists locally.
i.e. blow up a mountain on Planet XYZ, it will always remain blown up for you, but not any other player who visits Planet XYZ. This is because that particular information is saved locally. However, blow up a space station/port in System XYZ and it is lost to everyone (assuming you are connected to the net).