\(L\)-Mild Normality and \(L_2\)-Mild Normality

The purpose of this work is to introduce and study two new topological properties called \(L\)-mild normality and \(L_2\)-mild normality. A space \(X\) is called an \(L\)-mildly normal space if there exist a mildly normal space \(Y\) and a bijective function \(f:X\to Y\) such that the restriction function \(f|_A:A\to f(A) \) is a homeomorphism for each Lindelof subspace \(A\subseteq X\). If the space \(Y\) is Hausdorff, then the space \(X\) is called \(L_2\)-mildly normal. We investigate these properties and present some examples to illustrate the relationships among \(L\)-mild normality and \(L_2\)-mild normality with other kinds of topological properties.