Subsequences and Limits in R and R^n .... .... L&S Theorem 5.2 .... ....

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Theorem 5.2 from "Real Analysis: Foundations and Functions of One Variable" by Miklos Laczkovich and Vera T. Sos is confirmed to hold in $\mathbb{R}^k$, extending its applicability beyond $\mathbb{R}$. This theorem addresses the behavior of subsequences and limits in the context of infinite sequences. The discussion clarifies that the principles established in one-dimensional analysis are indeed relevant in higher dimensions, specifically in $\mathbb{R}^n$.

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  • Review examples of subsequences in $\mathbb{R}^n$ to solidify understanding of the theorem's application.
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In the book " Real Analysis: Foundations and Functions of One Variable" by Miklos Laczkovich and Vera T. Sos, Theorem 5.2 (Chapter 5: Infinite Sequences II) reads as follows:https://www.physicsforums.com/attachments/7722

Can someone inform me if there is an equivalent theorem that holds in $$\mathbb{R}^n$$?Peter
 
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Yes, Theorem 5.2 holds in $\Bbb R^k$, not just $\Bbb R$.
 

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