 Semitopology
Decentralised Collaborative Action via Topology, Algebra, and Logic
Murdoch J. Gabbay
We develop semitopologies, a new topological structure which gives a mathematical foundation to heterogeneous, decentralised, permissionless, computing systems. Semitopologies help to model consensus problems that commonly arise in designing cuttingedge peertopeer, blockchain, and other decentralised systems; especially when different such systems need to interact. Points correspond to participants in the system, and open sets correspond to the ways in which participants can cooperate.
This text is aimed at mathematicians and advanced students interested in a new topologyadjacent field with strong practical applications; and at engineers working to build decentralised systems who could use a mathematical foundation for designing the relevant tools. It aims to offer pleasant surprises and new ideas for researchers; and for practitioners, it aims to help build the next generation of better, safer, more scalable decentralised systems.
August 2024
9781848904651
