• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.69-86
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• 2019

In this paper, we introduce a concept of the ${\epsilon}_0$-limits of vector and multiple valued sequences in $R^m$. Using this concept, we study about the concept of the ${\epsilon}_0$-dense subset and of the points of ${\epsilon}_0$-dense ace in the open subset of $R^m$. We also investigate the properties and the characteristics of the ${\epsilon}_0$-dense subsets and of the points of ${\epsilon}_0$-dense ace.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.757-775
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• 2018

For any non-negative real number ${\epsilon}_0$, we shall introduce a concept of the ${\epsilon}_0$-dense subset of $R^m$. Applying this concept, for any sequence {${\epsilon}_n$} of positive real numbers, we also introduce the concept of the {${\epsilon}_n$}-attainable sequence and of the points of {${\epsilon}_n$}-attainable ace in the open subset of $R^m$. We also study the characteristics of those sequences and of the points of {${\epsilon}_n$}-dense ace. And we research the conditions that an {${\epsilon}_n$}-attainable sequence has no {${\epsilon}_n$}-attainable ace. We hope to reconsider the social consideration on the ace in social life by referring to these concepts about the aces.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.33-41
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• 2020

We introduced the concept of the 𝜖₀-density and the 𝜖₀-dense ace in [1]. This concept is related to the structure of employment. In addition to the double capacity theorem which was introduced in [1], we need the minimal dense subset. In this paper, we investigate a concept of the minimal 𝜖₀-dense subset in the Euclidean m dimensional space.