Regularity of topological and metric entropy of hyperbolic flows.
Regularity properties of functional equations.
Regularity properties of functional equations. (Short Communication).
Regularization of closed-valued multifunctions in a non-metric setting
Regular-uniform convergence and the open-open topology.
Related fixed points for set-valued mappings on two uniform spaces.
Relations among some closed graph and open mapping theorems
Relations approximated by continuous functions in the Vietoris topology
Let X be a Tikhonov space, C(X) be the space of all continuous real-valued functions defined on X, and CL(X×ℝ) be the hyperspace of all nonempty closed subsets of X×ℝ. We prove the following result: Let X be a locally connected locally compact paracompact space, and let F ∈ CL(X×ℝ). Then F is in the closure of C(X) in CL(X×ℝ) with the Vietoris topology if and only if: (1) for every x ∈ X, F(x) is nonempty; (2) for every x ∈ X, F(x) is connected; (3) for every isolated x ∈ X, F(x) is a singleton...
Relations between some topologies
Relations between ß X / X and a Certain Subspace of ... X.
Relatively realcompact sets and nearly pseudocompact spaces
A space is said to be nearly pseudocompact iff is dense in . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.
Relaxation theorem for set-valued functions with decomposable values
Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
Remark on ANR-divisors
Remark on completely Baire-additive families in analytic spaces
Remark on Raimi's theorem on translations
Remark on the Abstract Dirichlet Problem for Baire-One Functions
We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function....
Remarks on extremally disconnected semitopological groups
Answering recent question of A.V. Arhangel'skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.
Remarks on Hausdorff continuous multifunction and selections
Remarks on -subalgebras of
Let denote a subalgebra of which is closed under local bounded inversion, briefly, an -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of , we generalize the notion of -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of containing...
Remarks on Namioka spaces and R. E. Johnson's theorem on the norm seperability of the range of certain mappings.