- 1,789

- 4

**1. Homework Statement**

**Source**: An Introduction to Complex Analysis (Classical and Modern Approaches) by Wolfgang Tutschke and Harkrishan L. Vasudeva (Champan and Hall/CRC)

Ref. page 17

Consider the metric space [itex](\mathbb{C}, d)[/itex]

1. If [itex]U_{1}[/itex], [itex]U_{2}[/itex],....,[itex]U_{n}[/itex] are open sets in [itex]\mathbb{C}[/itex], then so is [tex]\bigcap_{k = 1}^{n} U_{k}[/tex].

2. If {[itex]U_{\alpha} : \alpha \in \Lambda[/itex]} is a collection of open sets in [itex]\mathbb{C}[/itex], where [itex]\Lambda[/itex] is any indexing set, then [tex]U = \bigcup_{\alpha \in \Lambda} U_{\alpha}[/tex] is also open.

**2. Homework Equations**

(None...all data stated in the question above)

**3. The Attempt at a Solution**

I am able to understand the proof of (1) but the proposition (2) is not clear to me.

What does an indexing set mean? Also, why does one need an indexing set in part (2) and not (1)?

Last edited: