On countable connected Hausdorff spaces in which the intersection of every pair of connected subsets is connected.
On countable Fréchet-Urysohn spaces
On countable locally connected spaces
On countably paracompact spaces and closed maps
On covering properties by regular closed sets.
On -property of strong spaces
It is shown that every strong space is a -space. In particular, it follows that every paracompact space is a -space.
On D-connected sets in the space
On dense subspaces satisfying stronger separation axioms
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...
On d-paracompactness and related properties
On -compactifications and -compactifiable spaces.
On -sequentially regular spaces
On Eberlein compactifications of metrizable spaces
We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.
On embeddings into where is Lindelöf
A.V. Arkhangel’skii asked that, is it true that every space of countable tightness is homeomorphic to a subspace (to a closed subspace) of where is Lindelöf? denotes the space of all continuous real-valued functions on a space with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace of ...
On expansions of a Urysohn space to a regular space.
On extension of functors to the Kleisli category of some weakly normal monads
The problem of extension of normal functors to the Kleisli categories of the inclusion hyperspace monad and its submonads is considered. Some negative results are obtained.
On extension of the group operation over the Čech-Stone compactification
The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension...
On extensions of fuzzy topologies
On extensions of uniformly continuous Banach-space-valued mappings
On factorization of maps through τX
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...