Each series
of real strictly positive terms gives rise to a topology on
by declaring
a proper subset
to be closed if
.
We explore the relationship between analytic properties of the series and topological
properties on
.
In particular, we show that, up to homeomorphism,
-many
topologies are generated. We also find an uncountable family of examples
with the property that for
any
, there is a continuous
bijection
, but the only
continuous functions
are constant.
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