Raster convergence with respect to a closure operator
Realization of Cartesian Closed Topological Hulls.
Realization of mappings
Realizations of topologies and closure operators by set systems and by neighbourhoods
Regular closure operators and compactness
Regular -spaces
Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics.
Relative continuity of the functor
Relative injectivity as cocompleteness for a class of distributors.
Remarks on reflections
Remarks on topologically algebraic functors
Representation of sheaves of metric lattices by sections
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...