Rational spaces and the property of universality
Real closed rings, I. Residue rings of rings of continuous functions
Realcompactification and repleteness of Wallman spaces.
Realcompactification of frames
We give a construction of Wallman-type realcompactifications of a frame by considering regular sub -frames the join of which generates . In particular, we show that the largest such regular sub -frame gives rise to the universal realcompactification of .
Realcompactness and spaces of vector-valued functions
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating...
Realcompactness and Wallman realcompactification
Rectangular covers of products missing diagonals
We give a characterization of a paracompact -space to have a -diagonal in terms of three rectangular covers of . Moreover, we show that a local property and a global property of a space are given by the orthocompactness of .
Recurrent and weakly recurrent points in G.
Recurrent functions and semigroups.
Recurrent functions on compact spaces.
Recurrent points and discrete points for elementary amenable groups.
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,...
Reflective functors via nearness
Reflexive families of closed sets
Let S(X) denote the set of all closed subsets of a topological space X, and C(X) the set of all continuous mappings f:X → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.
Regular and Other Kinds of Extensions of Topological Spaces
∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31] and of the...
Regular fuzzy spaces and fuzzy almost regular spaces
Regular representations of semisimple MV-algebras by continuous real functions
Regular -spaces
Regular spaces and relations