In this paper, we use the notion of upper set $\overline{R}(A)$ to define the local function and closure operator cl_R^*(A) in an ideal approximation space $(X,R,\mathcal{L})$. we introduce the interior and closure in ideal approximation spaces, generating two ideal approximation topological spaces based on minimal neighborhoods. The local functions of some subset $(A)$ of a universe $(X)$ with respect to a given ideal play a basic role in defining the related interior and closure operators. Separation axioms with respect to these ideal approximation spaces are reformulated and compared with examples to show their implications. We reformulate and study connectedness in these ideal approximation spaces and compare them with examples to show the implications between them. Ideal approximation and continuity are introduced. Moreover, we modified our definitions to get similar types of ideal approximation spaces but based on maximal neighborhoods. In addition, we explained the relationship between some of the topological properties of the two types with some examples.