Korean J. Math. Vol. 26 No. 4 (2018) pp.757-775
DOI: https://doi.org/10.11568/kjm.2018.26.4.757

The sequential attainability and attainable ace

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Buhyeon Kang


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.

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