Korean J. Math. Vol. 28 No. 3 (2020) pp.573-585
DOI: https://doi.org/10.11568/kjm.2020.28.3.573

On the generalized boundary and thickness

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Published: Sep 30, 2020
Keywords:
$\epsilon_{0}-$interior, $\epsilon_{0}-$exterior, $\epsilon_{0}-$boundary, $\epsilon_{0}-$thick
Mathematics Subject Classification:
03H05, 26E35

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Buhyeon Kang
Department of Mathematics, Seokyeong University Seoul 02713, Korea

Abstract

We introduced the concepts of the generalized accumulation points and the generalized density of a subset of the Euclidean space in [1] and [2]. 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.



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References

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