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

[Math Amateur]

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

 

[Euge]

Yes, Theorem 5.2 holds in $\Bbb R^k$, not just $\Bbb R$.