  The most general definition of a continuous function requires that the
preimage of any open set be open. Thus, to discuss continuity in the abstract,
it is necessary to first define a topology, which tells us which sets in a
space are open. Such a topology is given by three axioms that describe how the
open sets in a topology behave. In this paper we shall consider a change to one
of these axioms and determine how this change affects the continuity of a
function.
