Talk:Domain theory/Archive 1

False claim under Important result
I deleted the following claim from the section on important results:
 * A poset D with a least element is a dcpo if and only if every monotone function f on D has a fixed point.

This is false. Condsider for example D = {0,1,2,3,..., x,y,z} where the naturals are ordered as 0 <= 1 <= 2 ... and x, y, z are three "infinities" (above naturals) with x <= z, y <= z and x, y incomparable. Then every monotone function on D has a fixed point, but D is not a dcpo. Frege 07:25, 27 March 2007 (UTC)

Directed subset <> Directed set
The terms directed subset and directed set in this article seem to denote the same thing, viz. directed subset. According to directed set there is an important difference between these two, hence it seems that directed subset is what is really meant in this article. QplQyer (talk) 08:45, 24 February 2009 (UTC)