The euro opened the week up against the dollar in Europe, trading strongly against the U.S. currency, the Associated Press reported. The 15-nation currency was trading at US$1.5814 early Monday, up from the US$1.5775 it bought in late New York trading on Friday. The British pound climbed to US$1.9951, up from $1.9930 it bought in New York at the end of last week. The dollar slipped to 105.12 Japanese yen from 106.26 on Friday.