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...