Real-valued functions on Alexandroff (zero-set) spaces
Real-valued functions on certain semi-metric spaces
Recognition of certain classes of closed maps
Recognizing approximate -tameness.
Recurrent functions and semigroups.
Recurrent functions on compact spaces.
Reduction of Baire-measurability to uniform continuity
Refinable maps
Refinable maps in the theory of shape
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
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 Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces
2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.For weakly compact subsets of Hilbert spaces K, we study the existence of totally disconnected spaces L, such that C(K) is isomorphic to C(L). We prove that the space C(BH ) admits a Pełczyński decomposition and we provide a starshaped weakly compact K, subset of BH with non-empty interior in the norm topology, and such that C(K) ~= C(L) with L totally disconnected.Research partially supported by EPEAEK program “Pythagoras”....
Regular generalized -closed sets.
Regular maps and products of p-quotient maps
Regular measures and entropy on pseudo-compact spaces
Regular representations of semisimple MV-algebras by continuous real functions
Regular vector lattices of continuous functions and Korovkin-type theorems-Part I
We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive...
Regularity and extension of mappings in sequential spaces
Regularity and extension of maps