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Regularity and normality in hereditary bi m-spaces

Al-Omari Ahmad, Al Ghour Samer, Noiri Takashi

Demonstratio Mathematica

2022

Vol. 55, nr 1

226--237

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) .

About the ways of defining connected sets in the topological spaces

Domańska K., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2016

Vol. 21

11--16

A topological space is called connected if it is not the union of two disjoint, nonempty and open sets in this space. The standard exercises show that here the concept of open sets can be replaced by closed sets or separated sets. In this context we will discuss the definition of connected sets in topological spaces, not being the whole space with particular regard to metric spaces, without the term of subspace topology.