AN INTRODUCTION TO 𝜖₀-DENSITY AND 𝜖₀-DENSE ACE

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.