On left-separated compact spaces
On locales whose countably compact sublocales have compact closure
Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.
On Manes' countably compact, countably tight, non-compact spaces
We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.
On maps: Continuous, closed, perfect, and with closed graph.
On N. Noble's theorems concerning powers of spaces and mappings
On one-point -compactification and local - compactness
On order locally finite and closure-preserving covers
On -closed spaces.
On preimages of ultrafilters in ZF
We show that given infinite sets and a function which is onto and -to-one for some , the preimage of any ultrafilter of under extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model with a set of atoms and a finite-to-one onto function such that for each free ultrafilter of its preimage under does not extend to an ultrafilter. In addition, we show that in there exists an ultrafilter compact pseudometric...
On properties preserved by the approximate domination
On pseudocompact, countably compact, locally bicompact mappings, and -mappings.
On pseudocompactness and related notions in ZF
We study in ZF and in the class of spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.
On pushing out frames
On R-compact spaces
On regular and sigma-smooth two valued measures and lattice generated topologies.
On -cluster sets and -closed spaces.
On semicompact sets and associated properties.
On sets of confluent and related mappings in the space
On shapes of topological spaces
On some classes of compact spaces lying in -products