Can someone fence and openly use a part of someone else's land without their permission and in 10 years it belongs to them?

Squatters' rights no longer exists. It has been replaced by the law of adverse possession. In your case, if the person has fenced off the property and used it for a continuous period of 10 years, then yes, they may be able to sue for title to that property. You can read more about it at http://recenter.tamu.edu/pdf/1152.pdf

This law is also referred to as Open and Notorious possession. The true owner would also have to fail to do anything to get the "squatter" off his land within the time limits. In some caes the squatter must also be paying the taxes while the owner is not paying.

Why do you ask? Are you the land owner that had property infringed on or the infringer?