Internet speed is quite important at first, to download the blockchain.

Once you have downloaded the blockchain you can start mining and then the speed of the Internet is less important than the processing power of your computer.

Over time the blockchain will grow and you will need to have a higher Internet speed. However, that is a long way from happening.

http://www.ultrapoint.org/blockchain.html

http://www.ultrapoint.org/mining.html

http://www.ultrapoint.org/what-is-mining.html

http://www.ultrapoint.org/smart-mining.html

http://www.ultrapoint.org/ultrapoint-pools.html