A construction of the Gleason space
A factorization theorem and its application to extremally disconnected resolutions
A minimalization of 0-dimensional metric spaces
A note on extremally disconnected frames
A note on fixed points of a selfmap of an extremally disconnected space
A note on nowhere dense sets in
A note on the algebraic de Morgan's law
A tree -base for without cofinal branches
We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree -base for with no branches yet of height . We establish that this is also possible for using a natural modification of Mathias forcing.
Algebraic de Morgan's laws for non-commutative rings
Almost maximal topologies on groups
Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...
An open-perfect mapping on a hereditarily disconnected space onto a connected space