The pseudocircle is the finite topological space X consisting of four distinct points {a,b,c,d} with the following non-Hausdorff topology: { { a , b , c , d } , { a , b , c } , { a , b , d } , { a , b } , { a } , { b } , ∅ } . {\displaystyle \{\{a,b,c,d\},\{a,b,c\},\{a,b,d\},\{a,b\},\{a\},\{b\},\varnothing \}.} This topology corresponds to the partial order a < c , b < c , a < d , b < d {\displaystyle a<c,\ b<c,\ a<d,\ b<d} where the open sets are downward-closed sets.
The pseudocircle is the finite topological space X consisting of four distinct points {a,b,c,d} with the following non-Hausdorff topology: { { a , b , c , d } , { a , b , c } , { a , b , d } , { a , b } , { a } , { b } , ∅ } . {\displaystyle \{\{a,b,c,d\},\{a,b,c\},\{a,b,d\},\{a,b\},\{a\},\{b\},\varnothing \}.} This topology corresponds to the partial order a < c , b < c , a < d , b < d {\displaystyle a<c,\ b<c,\ a<d,\ b<d} where the open sets are downward-closed sets.
Source: Wikipedia "Pseudocircle" · CC BY-SA 4.0
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