on a set $X$
The topology in which every set is open (and therefore every set is closed). The discrete topology is the largest element in the lattice of all topologies on the given set. If $X$ is a space with the discrete topology, then every map from $X$ to any other topological space is continuous.
Discrete topology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discrete_topology&oldid=37244