On compactness with respect to semi-open sets
On countable Fréchet-Urysohn spaces
On D-dimension of metrizable spaces
For every cardinal τ and every ordinal α, we construct a metrizable space and a strongly countable-dimensional compact space of weight τ such that , and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of and to a subspace of .
On decomposition of spaces on meager sets
On elementary maps
On families of large oscillation
On families of Lindelöf and related subspaces of
We consider the families of all subspaces of size ω₁ of (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used...
On FU()-spaces and -sequential spaces
Following Kombarov we say that is -sequential, for , if for every non-closed subset of there is such that and . This suggests the following definition due to Comfort and Savchenko, independently: is a FU()-space if for every and every there is a function such that . It is not hard to see that ( denotes the Rudin–Keisler order) every -sequential space is -sequential every FU()-space is a FU()-space. We generalize the spaces to construct examples of -sequential...
On functions preserving almost radiality and their relations to radial and pseudo-radial spaces
On hereditarily separable Hausdorff spaces in the constructible universe
On hereditarily α-Lindelöf and α-separable spaces, II
On intersections of small perfect sets.
On left-separated compact spaces
On local merotopic character
On Luzin spaces
On minimal Hausdorff and minimal Urysohn functions
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
On monotone and pointwise splittability
On -in-countable bases
Some results concerning spaces with countably weakly uniform bases are generalized for spaces with -in-countable ones.
On natural merotopies
On nowhere first-countable compact spaces with countable -weight
The minimum weight of a nowhere first-countable compact space of countable -weight is shown to be , the least cardinal for which the real line can be covered by many nowhere dense sets.