Preface to the special issue for The Fifth Workshop on Formal Topology

THIERRY COQUAND, MARIA EMILIA MAIETTI, and ERIK PALMGREN

The paper introduces Formal Topology, which is a constructive approach to pointfree topology. Here we instead look at topologies with points, over finite sets and show:

• there is a unique topology on Fin 0;
• there is a unique topology on Fin 1;
• there exist two distinct topologies on Fin 2
• We also construct the remaining two topologies on Fin 2 giving a total of 4, and show they are homeomorphic.