Every Filter is Homeomorphic to Its Square

Andrea Medini, Lyubomyr Zdomskyy
2016 Bulletin of the Polish Academy of Sciences Mathematics  
We show that every filter F on ω, viewed as a subspace of 2 ω , is homeomorphic to F 2 . This generalizes a theorem of van Engelen, who proved that this holds for Borel filters. 2010 Mathematics Subject Classification: 54H99, 54E99, 03E05. . ( 1 ) Actually, van Engelen stated his results for ideals. Using the homeomorphism c : 2 ω → 2 ω defined by c(X)(n) = 1 − X(n) for X ∈ 2 ω and n ∈ ω, one sees that his results also hold for filters.
doi:10.4064/ba8065-6-2016 fatcat:7zegiih6efftxe5edzw2g7asce