On barycentrically soft compacta
On binary coproducts of frames
The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.
On category-raising and dimension-raising open mappings with discrete fibers
On c-closed functions
On Čech cohomology and weakly confluent mappings into ANR's
On -chain-net spaces.
On cliquish functions on product spaces
On closed and inductively closed images of products of metric spaces
On closed graph theorems in topological spaces and groups
On closed inverse images of base-paracompact spaces.
On closed mappings
On compact-covering and sequence-covering images of metric spaces
On confluently graph-like compacta
For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs, X is confluently...
On continuous images of almost Tychonoff cubes
On continuous maps in closure spaces.
On ℳ-contractibility
On countably paracompact spaces and closed maps
On decomposition of projections of finite order
On decompositions of continua
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...