Remarks on products of σ-ideals
Remarks on sequence covering images of metric spaces.
Remarks on star covering properties in pseudocompact spaces
Let be a topological property. A space is said to be star if whenever is an open cover of , there exists a subspace with property such that , where In this paper, we study the relationships of star properties for in pseudocompact spaces by giving some examples.
Remarks on the cardinality of a power homogeneous space
We provide a further estimate on the cardinality of a power homogeneous space. In particular we show the consistency of the formula for any regular power homogeneous ccc space.
Remarks on topologies uniquely determined by their continuous self maps
Representation of semigroups by products of topological spaces with prescribed cardinal functions
Representation Theorem for Minimal -Algebras
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
Representing free Boolean algebras
Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra...
RESIDUATION IN SEMIGROUPS OF PRE-CLOSURES.
Resolvability in c.c.c. generic extensions
Every crowded space is -resolvable in the c.c.c. generic extension of the ground model. We investigate what we can say about -resolvability in c.c.c. generic extensions for . A topological space is monotonically -resolvable if there is a function such that for each . We show that given a space the following statements are equivalent: (1) is -resolvable in some c.c.c. generic extension; (2) is monotonically -resolvable; (3) is -resolvable in the Cohen-generic extension ....
Results and problems concerning compactifications, compact subtopologies, and mappings
Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure.
R-fuzzy Strongly Preopen Sets in Fuzzy Topological Spaces
Right simple subsemigroups and right subgroups of compact convergence semigroups.
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...
Rings of Real-Valued Continuous Functions. II.
Rudin's Dowker space in the extension with a Suslin tree
We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same can be forced...
-closedness in -fuzzy topological spaces.