On 3-topological version of -regularity.
On a certain lattice of topologies on a product of metric spaces
On a product of metric spaces
On a property of the one-dimensional torus
On -open setes.
On cardinalities of row spaces of Boolean matrices.
On c-closed functions
On c-continuous fundamental groups
On co-lc topologies
On countable families of sets without the Baire property
We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property in X.
On coverings in the lattice of all group topologies of arbitrary Abelian groups.
On derivations of quantales
A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.
On generalized -closed sets.
On -continuity and -semicontinuity points
On lattices of generalized topologies
On Manes' countably compact, countably tight, non-compact spaces
We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.
On maximal chains in the lattice of module topologies.
On minimal strongly KC-spaces
In this article we introduce the notion of strongly -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space is maximal countably compact if and only if it is minimal strongly , and apply this result to study some properties of minimal strongly -spaces, some of which are not possessed by minimal -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether every...
On minimal--spaces
An -space is a topological space in which the topology is generated by the family of all -sets (see [N]). In this paper, minimal--spaces (where denotes several separation axioms) are investigated. Some new characterizations of -spaces are also obtained.
On modifications of topologies without axioms