On the axioms preserved by modifications of topologies without axioms
On the division by Rn.
On the Hausdorff Dimension of Topological Subspaces
It is shown that every Polish space X with admits a compact subspace Y such that where and denote the topological and Hausdorff dimensions, respectively.
On the pullback stability of a quotient map with respect to a closure operator.
On the simplicity of some categories of closure spaces
On the *topology and its application
On the topology generated by preopen sets
On the weight of nowhere dense subsets in compact spaces.
On topologies generated by some operators
The paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.
On treelike neighbourhood spaces
On U-equivalence spaces
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U- equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.
On --open sets and a decomposition of almost--continuity.
Operator decomposition of continuous mappings.
Operators associated to a topology over a set and related notions.
-regular Cauchy completions.
-topological Cauchy completions.
Partial dcpo’s and some applications
We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces , the corresponding partial dcpo’s of continuous real valued functions on are continuous partial dcpos; (iii) if a space is Hausdorff compact, the lattice of all S-lower semicontinuous functions on is the dcpo-completion of that of continuous real valued...
Pointless uniformities. I. Complete regularity
Pointless uniformities. II: (Dia)metrization
Pointwise convergence fails to be strict
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .