Exercise 9, § 4

General Topology, I, 127

Let $(X_i)_{i \in I}$ be an infinite family of topological spaces. Study the topology on the product set

X = \prod_{i \in I} X_i

generated by subsets of the form

\prod_{i \in I} U_i

, where

U_i

is an open subset of

X_i

for each

i \in I

and the set of indices

i

for which

U_i \neq X_i

has cardinal less than

c

, where

c

is a given infinite cardinal. Consider what becomes of the propositions of § 4 for this topology.

Solution

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