## The Theory of N-Scales

**Authors:** Furkan Semih Dundar

We provide a theory of $n$-scales previously called as $n$ dimensional time scales. In previous approaches to the theory of time scales, multi-dimensional scales were taken as product space of two time scales \cite{bohner2005multiple,bohner2010surface}. $n$-scales make the mathematical structure more flexible and appropriate to real world applications in physics and related fields. Here we define an $n$-scale as an arbitrary closed subset of $\mathbb R^n$. Modified forward and backward jump operators, $\Delta$-derivatives and multiple integrals on $n$-scales are defined.

**Comments:** 6 Pages. v3. Clarifications have been made.

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### Submission history

[v1] 2016-06-28 16:56:02

[v2] 2016-07-02 18:45:26

[v3] 2017-01-20 16:47:57

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