Regularity and normality in hereditary bi m-spaces

Abstract Quite recently, a new minimal structure m H ⋆ {m}_{H}^{\star } and an m n mn - ℋ g {{\mathcal{ {\mathcal H} }}}_{g} -closed set have been introduced in a previous study [T. Noiri and V. Popa, Closed sets in hereditary bi m-spaces, Questions Answers General Topol. 38 (2020), 133–142] by using two minimal structures m, n n and a hereditary class ℋ {\mathcal{ {\mathcal H} }} . In this paper, we introduce and investigate the notions of ( m , n ) \left(m,n) - ℋ g ⋆ {{\mathcal{ {\mathcal H} }}}_{g}^{\star } -regularity and ( m , n ) \left(m,n) - ℋ g ⋆ {{\mathcal{ {\mathcal H} }}}_{g}^{\star } -normality in a hereditary bi m-space ( X , m , n , ℋ ) \left(X,m,n,{\mathcal{ {\mathcal H} }}) .