Since it is in regards with the Premier League, There are many teams that have not been relegated from it They are: Arsenal, Aston Villa, Blackpool, Chelsea, Fulham, Liverpool. Manchester united, Stoke City, Tottenham Hotspurs, And Wigan Athletic.
If you mean in the same year, then Bolton, Blackburn and Fulham were all promoted in 2001 and all have not been relegated since (as of 2011)
Manchester united have never been relegated from the premier league. in 1974 they were relegated from the old first division
Arsenal have never been relegated.
Arsenal FC have never been relegated from the Premier League but were relegated to the then Fourth Division (modern League Two) in 1913.
Arsenal never was relegated.
They have never been relegated from the Premier League. Since the Premier League was founded in 1992 they ended 11th position in 1992/1993 but have never been relegated.