Definition 1. An open semioroup ~ of ~3 will be called an F-semigroup/f (i) a, b ~ ~3 and ab = ba E ~ imply a ~ ~ and b ~ ~, and (ii) there exists a closed ideal R such that ~ = q-1 (S), where S is an open semigroup in ~B/R containin 9 G and havin 9 the property that S\G is also open. It is clear that ~ contains the invertible elements of ~B, and that ~+-qc~. (1-1) If a ~ ~ and if~a is the (maximal connected open) component of~ containing a, then a + R C ~a.