- #1

Math Amateur

Gold Member

MHB

- 3,998

- 48

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

I need help with an aspect of Lemma 1.2.5 (ii) ...

Duistermaat and Kolk"s statement and proof of Lemma 1.2.5 reads as follows: View attachment 7673My question regarding Lemma 1.2.5 is as follows:

Lemma 1.2.5 (ii) is stated and proved only for a finite collection of open subsets of \(\displaystyle \mathbb{R}^n\) ... but why do we restrict the result to finite collections of open subsets ... there must be a problem with the infinite collection case ... but D&K give no explanation of why this is so ...

Can someone please explain the difficulty with the infinite collection case ...

Hope someone can help ...

Peter