On bitopological full normality
On bitopological local compactness
On bitopological separation axioms
On Blumberg type spaces
On boundedness in uniform spaces
On butterfly-points in , Tychonoff products and weak Lindelöf numbers
Let be the Tychonoff product of -many Tychonoff non-single point spaces . Let be a point in the closure of some whose weak Lindelöf number is strictly less than the cofinality of . Then we show that is not normal. Under some additional assumptions, is a butterfly-point in . In particular, this is true if either or and is infinite and not countably cofinal.
On categories of supertopological spaces
On category-raising and dimension-raising open mappings with discrete fibers
On certain homological properties of finite-dimensional compacta. Carriers, minimal carriers and bubbles
On certain porous sets in the Orlicz space of a locally compact group
Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces and on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set is well defined on G is σ-c-lower porous in . This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.
On certain properties characterizing locally separable metric spaces
On certain types of convergences
Mappings preserving Cauchy sequences and certain types of convergences connected with these mappings are investigated.
On character of points in the Higson corona of a metric space
We prove that for an unbounded metric space , the minimal character of a point of the Higson corona of is equal to if has asymptotically isolated balls and to otherwise. This implies that under a metric space of bounded geometry is coarsely equivalent to the Cantor macro-cube if and only if and . This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic.
On Ciric's fixed point theorem
On classification of weakly infinite-dimensional compacta
On cliquish functions on product spaces
On closed and inductively closed images of products of metric spaces
On closed mappings
On clusters in proximity spaces
On coarse embeddability into -spaces and a conjecture of Dranishnikov
We show that the Hilbert space is coarsely embeddable into any for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into are equivalent for 1 ≤ p < 2.