Remark on completely Baire-additive families in analytic spaces
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....
Remark on topological embedding of commutative mappings
Remark on topological spaces with given semigroups
Remarks on a fixed-point theorem of Gerald Jungck.
Remarks on a game of Choquet
Remarks on best approximation in R-trees
An R-tree is a geodesic space for which there is a unique arc joining any two of its points, and this arc is a metric segment. If X is a closed convex subset of an R-tree Y, and if T: X → 2Y is a multivalued mapping, then a point z for which [...] is called a point of best approximation. It is shown here that if T is an ε-semicontinuous mapping whose values are nonempty closed convex subsets of Y, and if T has at least two distinct points of best approximation, then T must have a fixed point. We...
Remarks on certain selected fixed point theorems.
Remarks on cone metric spaces and fixed point theorems of contractive mappings.
Remarks on coupled fixed point theorem in cone metric spaces
Remarks on density topology and its category analogue
Remarks on extensions of the Himmelberg fixed point theorem.
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 -density and -approximately continuous functions
Remarks on Lipschitzian mappings and some fixed point theorems.
Remarks on recent fixed point theorems.
Remarks on recent fixed point theorems for compatible maps.
Remarks on some fixed point theorems.
Remarks on some generalizations of asymptotic periodicity in dynamical systems on metric spaces
Remarks on the region of attraction of an isolated invariant set
We study the complexity of the flow in the region of attraction of an isolated invariant set. More precisely, we define the instablity depth, which is an ordinal and measures how far an isolated invariant set is from being asymptotically stable within its region of attraction. We provide upper and lower bounds of the instability depth in certain cases.