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.
Countably compact spaces all countable subsets of which are scattered
Countably -compact spaces.
Countably -closed spaces