Thanks for the input.
To clarify, yes I am willing to pay and basically have my own internet connection in this apartment. The shared internet in the building is corporate with Fibercorp, I don't know the details other than the lady owns the whole building and all the apartments. It's not good enough for me so I want to pay to have an extra personal internet connection (my own) seperately. I, of course, would be paying for this myself because it is my service.
I am not sure if she will be willing to do it because I don't know if setting up that service would require any work such as drilling, holes in walls etc. If it would not then I think she may allow it, or I may be tempted just to go ahead and get it anyway. I mean, there is nowhere in the contract that says I cannot get additional internet.
I also think she in no way would share the costs. If she wanted better internet she would alreaday have it, I guess.