As requirements for our work, we define here the following concepts sequentially:
Ideal space, local function, Kuratowski closure, dense, T*-dense, I-dense, codense,
?-operator, resolvable, I-open, pre-I-open, scattered set and Housdorff space.
We start define the ideal space. Let (X, T) be a topological space with no separation
properties assumed. The subject of ideal topological space has been studied by
(Kuratowski, 1966) and (Vaidyanathaswamy, 1960). An ideal I on a topological space
(X, T) is a nonempty collection of subsets of X which satisfies the following two
conditions:
)1) If A ? I and B ? A, then B? I (heredity).
(2) If A? I and B? I, then A? B? I (finite additivity).
Moreover a ?-ideal on a topological space (X, T) is an ideal which satisfies (1), (2) and
the following condition:
3.If {Ai : i = 1,2,3,….} ? I, then ? {Ai : i =1,2,3,….} ? I (countable additivity