2021/01/02 by Piotr Borodulin–Nadzieja, Borodulin-Nadzieja, Piotr, Damian Sobota +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2101.00513
openalex publication_date 2021/01/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
For given Boolean algebras mathbbA and mathbbB we endow the space\n\H( mathbbA, mathbbB) of all Boolean homomorphisms from\n mathbbA to mathbbB with various topologies and study convergence\nproperties of sequences in \H( mathbbA, mathbbB). We are in\nparticular interested in the situation when mathbbB is a measure algebra\nas in this case we obtain a natural tool for studying topological convergence\nproperties of sequences of ultrafilters on mathbbA in random extensions of\nthe set-theoretical universe. This appears to have strong connections with Dow\nand Fremlin's result stating that there are Efimov spaces in the random model.\nWe also investigate relations between topologies on\n\H( mathbbA, mathbbB) for a Boolean algebra mathbbB\ncarrying a strictly positive measure and convergence properties of sequences of\nmeasures on mathbbA.\n