McCoy introduced a
topology intermediate between the Tikhonov and box product topologies on the
countably infinite power ωX of a topological space X. He used this topology to study
Baire category in 2X, the hyperspace of closed subsets of X in the Vietoris topology.
In this note we generalize this ‘pinched-cube’ topology to arbitrary infinite powers,
κX, of X and investigate the extent to which it inherits fundamental properties of
X.
In §1 we introduce basic definitions and elementary facts. Separation axioms are
considered in §2, compactness, connectedness, and separability in §3. In §4 we
consider some completeness properties, and in §5 we explicate the connection with
hyperspaces.
