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
C- and C*-quotients in pointfree topology [Book]
Cardinal functions on compact F-spaces and on weakly countably complete Boolean algebras
Closed and open sets in topologies induced by lattice ordered vector groups
Coherent ultrafilters and nonhomogeneity
We introduce the notion of a coherent -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a -point on , and show that these ultrafilters exist generically under . This improves the known existence result of Ketonen [On the existence of -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1, 233–241] can...
Compact and extremally disconnected spaces.
Compact sets without converging sequences in the random real model.
Completeness properties of function rings in pointfree topology
This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.
Continuous images of which are homeomorphic to .
Coronas of ultrametric spaces
We show that, under CH, the corona of a countable ultrametric space is homeomorphic to . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.