Coherence of Semifilters

by T.Banakh and L.Zdomsky

   The book is devoted to studying the (sub)coherence relation on semifilters, that is families of infinite subsets of ω, closed under taking almost supersets. On the family of ultrafilters the coherence relation was introduced in 80-ies by A.Blass who formulated his famous principle (NCF), the Near Coherence of Filters, that found many non-trivial applications in various fields of mathematics.
   In the book the (sub)coherence relation is treated with help of cardinal functions defined on the lattice SF of semifilters.
   Endowed with the Lawson topology the lattice SF becomes a supercompact topological space. It can be interesting for topological algebraists because any reasonable binary operation on natural numbers induces a right-topological operation on SF in the same way as it does on the Stone-Cech compactification βω.


This is a preliminary version of the book. So the authors would appreciate any remarks, comments, and suggestions. You can write to the authors by e-mail