The present work is concerned with the new space namely ideal \(\mathcal{L}-\) space. It is accordingly devoted to the basic properties of this new space and the relation between open set, \(\mathcal{L}-\) open set and \({\mathcal{L}}^{*}-\) open set are studied as well as the concept of \(\mathcal{L}-\) local function and some of their basic properties, examples and characterizations are presented. If \(\mathfrak{F}\) is topology on \(\mathcal{X}\) , then \(\mathcal{H}\) is \(\mathcal{L}-\) open set if \(\mathcal{H}\subseteq T\bigcup Int\left(\mathcal{H}\right)\) \(\forall T\in \mathfrak{F} \& T\ne\Phi \) . The \(\mathcal{L}-\) kuratowski closure operator for any subset \(\mathcal{A}\) of \(\mathcal{X}\) with respect to \({\mathcal{I}}_{\mathcal{X}}\) and \({\mathcal{L}O}_{\mathcal{X}}\) is defined as \({cl}_{\mathcal{L}}^{*}\left(\mathcal{A}\right)=\mathcal{A}\bigcup {\mathcal{A}}_{\mathcal{L}}^{*}\) . The \(\mathcal{L}-\) closure of \(\mathcal{H}\subseteq \mathcal{X}\) is denoted by \({cl}_{\mathcal{L}}(\mathcal{H})\) and it is the intersection for every \(\mathcal{L}-\) closed sets that contains \(\mathcal{H}\) . Furthermore, this paper contains a study of some concepts in ideal \(\mathcal{L}-\) space such as \(\mathcal{L}-\) dense set and \({\mathcal{I}}_{\mathcal{X}}-\mathcal{L}-\) dense set as well as characterizations and examples of the proposed idea are given. Finally, we studying the definition of \(\mathcal{L}-\) dense set and \(\mathcal{L}-\) codense set in order to introduce the concept of \(\mathcal{L}-\) codense ideal and some important results related to these concepts are proven.