Original sentence: An important class of pointwise concepts are the pointwise operations — operations defined on functions by applying the operations to function values separately for each point in the domain of definition.In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value  of some function  An example is pointwise convergence of functions — a sequence of functions.These include
Edited sentence: An example of infinitary pointwise relation is pointwise convergence of functions — a sequence of functions.Blyth, Lattices and Ordered Algebraic Structures, Springer, 2005, ISBN 1-85233-905-5.Examples include.For instance if A and B are continuous lattices, the so is then set of functions A → B with pointwise order.For order theory examples:.Gierz, K.Hofmann, K.Important relations can also be defined pointwise.In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value  of some function  An important class of pointwise concepts are the pointwise operations — operations defined on functions by applying the operations to function values separately for each point in the domain of definition.In order theory it is common to define a pointwise partial order on functions.Keimel, J.Lawson, M.Mislove, D.Pointwise orders also inherit some properties of the underlying posets.Scott: Continuous Lattices and Domains, Cambridge University Press, 2003.With A, B posets, the set of functions A → B can be ordered by f ≤ g if and only if (∀x ∈ A) f(x) ≤ g(x)