Semitopology. Decentralised Collaborative Action via Topology Algebra and Logic

<p><br></p><p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>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 cutting-edge peer-to-peer 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.</span></p><p><br></p><p><span style=background-color: rgba(237 237 228 1); color: rgba(0 0 0 1)>This text is aimed at mathematicians and advanced students interested in a new topology-adjacent 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.</span></p>