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I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ...

I am focused on Chapter 1: Continuity ... ...

I need help with an aspect of Lemma 1,1,7 (ii) ...

Duistermaat and Kolk"s Lemma 1.1.7 reads as follows:

View attachment 7640

View attachment 7641

In the above Lemma part (ii), Duistermaat and Kolk refer to \(\displaystyle x^{ (k) }\) ... but what does \(\displaystyle x^{ (k) }\) mean ... ? ... is it \(\displaystyle x\) to the power \(\displaystyle k\) ... ? ... ... what exactly does it mean ... indeed, why are there parentheses around k ... ... ... and further, how do we interpret or make sense of part (ii) ...Help will be appreciated ...

Peter

I have searched, but cannot find an explanation by Duistermaat and Kolk of a notation in which there are parentheses around the exponent ...

I am focused on Chapter 1: Continuity ... ...

I need help with an aspect of Lemma 1,1,7 (ii) ...

Duistermaat and Kolk"s Lemma 1.1.7 reads as follows:

View attachment 7640

View attachment 7641

In the above Lemma part (ii), Duistermaat and Kolk refer to \(\displaystyle x^{ (k) }\) ... but what does \(\displaystyle x^{ (k) }\) mean ... ? ... is it \(\displaystyle x\) to the power \(\displaystyle k\) ... ? ... ... what exactly does it mean ... indeed, why are there parentheses around k ... ... ... and further, how do we interpret or make sense of part (ii) ...Help will be appreciated ...

Peter

***** NOTE *****

I have searched, but cannot find an explanation by Duistermaat and Kolk of a notation in which there are parentheses around the exponent ...

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