A countably compact, separable space which is not absolutely countably compact
We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.
A counterexample in non-metric continua theory
A decomposition theorem for compact groups with an application to supercompactness
We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.
A direct description of uniform completion in locales and a characterization of -groups
A Dowker group
A few topological problems
A first countable supercompact Hausdorff space with a closed nonsupercompact subspace
A function space C(X) which is weakly Lindelöf but not weakly compactly generated
A function which preserves connected spaces
A game and its relation to netweight and D-spaces
We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
A general "in between theorem".
A general invariant metrization theorem for compact spaces
A general realcompactification method
A generalisation of almost-compactness, with an associated generalisation of completeness
A generalisation of normal spaces
A generalization of Čech-complete spaces and Lindelöf -spaces
The class of -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf -spaces, metrizable spaces with the weight , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that -spaces are in a duality with Lindelöf -spaces: is an -space if and only if some (every) remainder of in a compactification is a Lindelöf -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. 220 (2013),...
A Generalization of Chain-net Spaces
A generalization of -compact spaces
A generalization of Magill's Theorem for non-locally compact spaces
In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the...
A generalization of N. Aronszajn's theorem on connectedness of the fixed point set of a compact mapping