Quite recently, a new minimal structure m⋆H and an mn - Hg -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 and a hereditary class H . In this paper, we introduce and investigate the notions of (m,n) - H⋆g -regularity and (m,n) - H⋆g -normality in a hereditary bi m-space (X,m,n,H) .
We introduce the notion of (i, j)-mI-open sets as a unified form of (i, j)-α-I-open sets [4], (i, j)-semi-I-open sets [3], (i, j)-pre-I-open sets [1], (i, j)-bI-open sets [17] and (i, j)-β-I-open sets [2]. We show that properties of (i, j)-mI-open sets follow from the properties of minimal open sets in [14]. We introduce and investigate an (i, j)-mI-continuous function from an ideal bitopological space (X, τ1, τ2, I) to a bitopological space (Y, σ1, σ2).
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In this paper, we introduce the notion of contra (mX, mY)-semicontinuous functions between m-spaces. We obtain many characterizations of these functions and deal with decompositions of the functions and other related functions.
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