Real closed rings, I. Residue rings of rings of continuous functions
Real ideals in the maximal ring of quotients of
Realisierung und Auswahlaxiom
Realizations of topologies and closure operators by set systems and by neighbourhoods
Refining Families for Ultrafilters.
Reflecting character and pseudocharacter
We say that a cardinal function reflects an infinite cardinal , if given a topological space with , there exists with . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with...
Reflecting Lindelöf and converging ω₁-sequences
We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition,...
Reflecting topological properties in continuous images
Given a topological property P, we study when it reflects in small continuous images, i.e., when for some infinite cardinal κ, a space X has P if and only if all its continuous images of weight less or equal to κ have P. We say that a cardinal invariant η reflects in continuous images of weight κ + if η(X) ≤ κ provided that η(Y) ≤ κ whenever Y is a continuous image of X of weight less or equal to κ +. We establish that, for any infinite cardinal κ, the spread, character, pseudocharacter and Souslin...
Reflective functors via nearness
Regular and normal quantales
Regular Convergence Spaces.
Regular fuzzy spaces and fuzzy almost regular spaces
Regular generalized -closed sets.
Regular -fuzzy topological spaces and their topological modifications.
Regular -spaces
Regular spaces of small extent are ω-resolvable
We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular...
Regularity and extension of mappings in sequential spaces
Regularity and extension of maps
Regularity and normality on L-topological spaces. I.
Regularity in convergence spaces