## Possible Topologies on a Set With Three Elements

Suppose we have a setconsisting of three elements

A group consisting of sets of elements ofis a topologyif

for any two open sets

for any two open sets

With these conditions the possible topologies are

Suppose we have a setconsisting of three elements

A group consisting of sets of elements ofis a topologyif

for any two open sets

for any two open sets

With these conditions the possible topologies are