Remarks on chain conditions in products
Remarks on discretely absolutely star-Lindelöf spaces
Remarks on reflections
Remarks on Star-Hurewicz Spaces
A space X is star-Hurewicz if for each sequence (𝒰ₙ: n ∈ ℕ) of open covers of X there exists a sequence (𝓥ₙ: n ∈ ℕ) such that for each n, 𝓥ₙ is a finite subset of 𝒰ₙ, and for each x ∈ X, x ∈ St(⋃ 𝓥ₙ,𝒰ₙ) for all but finitely many n. We investigate the relationship between star-Hurewicz spaces and related spaces, and also study topological properties of star-Hurewicz spaces.
Remarks on subsets of Cartesian products of metric spaces
Remarks on the Stone Spaces of the Integers and the Reals without AC
In ZF, i.e., the Zermelo-Fraenkel set theory minus the Axiom of Choice AC, we investigate the relationship between the Tychonoff product , where 2 is 2 = 0,1 with the discrete topology, and the Stone space S(X) of the Boolean algebra of all subsets of X, where X = ω,ℝ. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.
Remarks on topologically algebraic functors
Remarks on topologies uniquely determined by their continuous self maps
Removing sets from connected product spaces while preserving connectedness
As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results...
Representation of semigroups by products of topological spaces with prescribed cardinal functions
Representation of sheaves of metric lattices by sections
Representations into the hyperspace of a compact group.
Representations of commutative semigroups by products of metric -dimensional spaces
Representations of countable commutative semigroups by products of weakly homogeneous spaces
Representations of presheaves of closure space
Representations of presheaves of semiuniformisable spaces, and representation of a presheaf by the presheaf of all continuous sections in its covering-space
Resolutions of spaces and proper inverse systems in shape theory
Resolutions Of Spaces Are Strong Expansions
Ring epimorphisms and .
Rings of maps: sequential convergence and completion
The ring of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring of all continuous functions and, similarly, the ring of all Borel measurable subsets of is a sequential ring completion of the subring of all finite unions of half-open intervals; the two completions are not categorical. We study -rings of maps and develop a completion theory covering the two examples. In particular, the -fields of sets form an epireflective...