In order theory, a continuous poset is a partially ordered set in which every element is the directed supremum of elements approximating it. Let a , b...

elements x, y of X, at least one of x R y or y R x holds. Continuous poset. A poset is continuous if it has a base, i.e. a subset B of P such that every...

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function...

branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered...

basis is also called a continuous ω-cpo (or continuous dcpo). Note that complete partial order is never used to mean a poset in which all subsets have...

of a poset for obtaining these directed sets, then the poset is even algebraic. Both concepts can be applied to lattices as follows: A continuous lattice...

Dedekind completion Ideal completion Way-below relation Continuous poset Continuous lattice Algebraic poset Scott domain Algebraic lattice Scott information...

(transitivity). A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these...

directed join. When Q {\displaystyle Q} is the poset of truth values, i.e. Sierpiński space, then Scott-continuous functions are characteristic functions of...

functions between topological spaces Scott continuity, for functions between posets Continuity (set theory), for functions between ordinals Continuity (category...