Distinguishing Lindelöfness and inverse Lindelöfness
On a Hausdorff inverse Lindelöf non Lindelöf topology has been constructed.
Nowhere dense subsets and Booth's Lemma
The following statement is proved to be independent from : Let be a Tychonoff space with and . Then a union of less than of nowhere dense subsets of is a union of not greater than of nowhere dense subsets.
is not subsequential
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its -space is not subsequential.
Irresolvable countable spaces of weight less than
We construct in Bell-Kunen’s model: (a) a group maximal topology on a countable infinite Boolean group of weight and (b) a countable irresolvable dense subspace of . In this model .
Oб одной задаче Э. Чеха
On countable Fréchet-Urysohn spaces
The sequentiality and the Fréchet-Urysohn property with respect to ultrafilters
Tightness and resolvability
We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.
Structure resolvability
We introduce the general notion of structure resolvability and structure irresolvability, generalizing the usual concepts of resolvability and irresolvability.
The sequentiality is equivalent to the -Fréchet-Urysohn property
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