Abstract Stone Duality and Bitopological Spaces in Domain Theory

This course conducts a rigorous, axiomatic reconstruction of topology from the perspective of Paul Taylor's Abstract Stone Duality (ASD), entirely eschewing point-set foundations. The programme proceeds by first developing the synthetic theory of the Sierpiński space in a category equipped with a dominance, then specialising to the bitopological case where a closed and an open topology coexist on the same carrier.