On strongly measure replete lattices and the general Wallman remainder
On Szymański theorem on hereditary normality of
We discuss the following result of A. Szymański in “Retracts and non-normality points" (2012), Corollary 3.5.: If is a closed subspace of and the -weight of is countable, then every nonisolated point of is a non-normality point of . We obtain stronger results for all types of points, excluding the limits of countable discrete sets considered in “Some non-normal subspaces of the Čech–Stone compactification of a discrete space” (1980) by A. Błaszczyk and A. Szymański. Perhaps our proofs...
On tensor products of continuous functions
On the characterization of weak closure in Hilbert space
On the compactification of closure algebras
On the existence of P-points in the Stone-Čech compactification of integers
On the maximal -compactification of products of two -spaces.
On the Nachbin compactification of products of totally ordered spaces.
On the two natural products in a Stone-Cech compactification .
On thick spaces
On unitary Cauchy filters on topological monoids
For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A distant purpose...
On unitary extensions and unitary completions of topological monoids
The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.
One-point compactification on convergence spaces.
One-point compactifications of intuitionistic locally compact spaces
Open and closed mappings and compactification
Openly factorizable spaces and compact extensions of topological semigroups
We prove that the semigroup operation of a topological semigroup extends to a continuous semigroup operation on its Stone-Čech compactification provided is a pseudocompact openly factorizable space, which means that each map to a second countable space can be written as the composition of an open map onto a second countable space and a map . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.
Operator compactification of topological spaces.
Ordered Cauchy spaces.
Ordered compactification of totally ordered spaces.
Ordered compactifications and families of maps.