| Summary: | Quite recently, a new minimal structure mH⋆{m}_{H}^{\star } and an mnmn-ℋg{{\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, nn and a hereditary class ℋ{\mathcal{ {\mathcal H} }}. In this paper, we introduce and investigate the notions of (m,n)\left(m,n)-ℋg⋆{{\mathcal{ {\mathcal H} }}}_{g}^{\star }-regularity and (m,n)\left(m,n)-ℋg⋆{{\mathcal{ {\mathcal H} }}}_{g}^{\star }-normality in a hereditary bi m-space (X,m,n,ℋ)\left(X,m,n,{\mathcal{ {\mathcal H} }}).
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