Theorem 20.5 in Munkres Topology Book

[ehrenfest]

[SOLVED] munkres question

Homework Statement

Please stop reading unless you have Munkres topology book.
In Theorem 20.5, what is i? Are they assuming the index set omega is countable?

Homework Equations

The Attempt at a Solution

 

[morphism]

Yes. $\mathbb{R}^{\omega}$ is used to denote the set of all sequences of reals, see page 38. In general, $\omega$ is used to denote the smallest infinite ordinal, and hence is associated with countably infinite products and such.