## 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:

 2.6e+36 Nonstandard analysis

Zbl 1477.26047
Full Text:

### 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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.