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On the generalized boundary and thickness. (English) Zbl 1477.26048

Summary: We introduced the concepts of the generalized accumulation points and the generalized density of a subset of the Euclidean space in [B. Kang, “An introduction to \(\epsilon_0\)-density and \(\epsilon_0\)-dense ace”, J. Chung. Math. Soc. 32, No. 1, 69–86 (2019; doi:10.14403/jcms.2019.32.1.69)] and [B. Kang, Korean J. Math. 26, No. 4, 757–775 (2018; Zbl 1477.26047)]. Using those concepts, we introduce the concepts of the generalized closure, the generalized interior, the generalized exterior and the generalized boundary of a subset and investigate some properties of these sets. The generalized boundary of a subset is closely related to the classical boundary. Finally, we also introduce and study a concept of the thickness of a subset.

MSC:

26E35 Nonstandard analysis

Citations:

Zbl 1477.26047
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References:

[1] Buhyeon Kang, An Introduction to ε0-Density and ε0-Dense Ace, JCMS. 32 (1) (2019).
[2] Buhyeon Kang, The sequential attainability and attainable ace, Korean J. Math. 26 (4)(2018). · Zbl 1477.26047
[3] Yong Chan Kim and Jung Mi Ko, The properties of rough approximations, Ko- rean J. Math. 19 (2)(2011).
[4] Yong Chan Kim and Jung Mi Ko, L-fuzzy bi-closure systems and L-fuzzy bi- closure operators, Korean J. Math. 27 (2) (2019). · Zbl 1477.06042
[5] Shyamapada Modak and Ahmad Abdullah Al-omari, Generalized Closed Sets in Binary Ideal Topological Spaces, JCMS. 31 (1) (2018).
[6] M.Bala Prabhakar, S.Kalesha Vali, and M. Sambasiva Rao, Closed and Dense Elements of BE-algebras, JCMS. 32 (1) (2019).
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