For a minimal example consider the following two 3-element posets equipped with the Alexandroff topology (i.e. open sets are down-sets):

```
(a) (b) (C)
\ / / \
\ / / \
(c) (A) (B)
```

The bijection is given by: $a\mapsto A$, $b\mapsto B$, $c\mapsto C$.

The reconstruction conjecture for ordered sets (see e.g. Jean-Xavier Rampon, *What is reconstruction for ordered sets?*) - together with equivalence of finite posets and finite $T_0$ topological spaces (via the specialization order/Alexandroff topology functors) - says the are no such examples among finite $T_0$ spaces with at least **four** elements. However, the conjecture is open.

(The related reconstruction conjecture for graphs is better known and also open.)