The discrete topology on a set 
is the topology in which every
subset is an open set. This
is the largest topology on 
. The smallest topology has just
the open sets consisting of the empty
set 
and 
,
which are distinct when 
is nonempty. In particular,
every singleton set 
with 
is an open set in the discrete
topology.
Discrete Topology
See also
Discrete Mathematics, Discrete Set, Topological SpacePortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Discrete Topology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DiscreteTopology.html