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

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.


$\epsilon_{0}$-dense, $\{ \epsilon_{n}\}$-attainable sequence, $\{ \epsilon_{n}\}$-attainable ace

Subject classification

03H05, 26E35


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