Every Filter is Homeomorphic to Its Square
Tom 64 / 2016
Bulletin Polish Acad. Sci. Math. 64 (2016), 63-67
MSC: 54H99, 54E99, 03E05.
DOI: 10.4064/ba8065-6-2016
Opublikowany online: 8 July 2016
Streszczenie
We show that every filter $\mathcal {F}$ on $\omega $, viewed as a subspace of $2^\omega $, is homeomorphic to $\mathcal {F}^2$. This generalizes a theorem of van Engelen, who proved that this holds for Borel filters.
