AbstractLet ∅≠T⊂R, (X,d,+) be an additive commutative semigroup with metric d satisfying d(x+z,y+z)=d(x,y) for all x,y,z∈X, and XT the set of all functions from T into X. If n∈N and f,g∈XT, we set ν(n,f,g,T)=sup∑i=1nd(f(ti)+g(si),g(ti)+f(si)), where the supremum is taken over all numbers s1,…,sn,t1,…,tn from T such that s1⩽t1⩽s2⩽t2⩽⋯⩽sn⩽tn. We prove the following pointwise selection theorem: If a sequence of functions {fj}j∈N⊂XT is such that the closure in X of the set {fj(t)}j∈N is compact for each t∈T, andlimn→∞(1nlimN→∞supj,k⩾N,j≠kν(n,fj,fk,T))=0, then it contains a subsequence which converges pointwise on T. We show by examples that this result is sharp and present two of its variants
summary:We introduce the spaces $M^{1}_{Y,\varphi }$, $M^{o,n}_{Y,\varphi }$, $\tilde{M}^{o}_{Y,\var...
AbstractWe prove a continuous selection theorem for quasi-lower semicontinuous mappings with values ...
Let H be a Hilbert space. Let ...
AbstractLet T be a nonempty set of real numbers, X a metric space with metric d and XT the set of al...
AbstractLet X be a metric space with metric d, c(X) denote the family of all nonempty compact subset...
AbstractGiven a=(a1,…,an), b=(b1,…,bn)∈Rn with a<b componentwise and a map f from the rectangle Iab=...
Let $\emptyset\neq T \subset \RB, \hspace{.1in} (X,d,+)$ be an additive commutative semigroup with m...
Let $T$ be a nonempty subset of $\RB$, $X$ a metric space with metric $d$ and $X^T$ the set of all f...
AbstractUsing the ‘multiplied’ version of Helly's theorem given by Bárány (Discrete Math. 40 (1982) ...
In this note we consider oscillation of regulated functions. We improve and simplify the proof of th...
Let USCp ⋆(X) be the topological space of real upper semicontinuous bounded functions defined on X w...
contains corrections with respect to published version.We provide a simple proof of a result which g...
For a Tychonoff space X, Cp(X) is the space of all real-valued continuous functions with the topolog...
summary:We compare a recent selection theorem given by Chistyakov using the notion of modulus of var...
AbstractWe prove that certain classes of sequences of positive real numbers satisfy some selection p...
summary:We introduce the spaces $M^{1}_{Y,\varphi }$, $M^{o,n}_{Y,\varphi }$, $\tilde{M}^{o}_{Y,\var...
AbstractWe prove a continuous selection theorem for quasi-lower semicontinuous mappings with values ...
Let H be a Hilbert space. Let ...
AbstractLet T be a nonempty set of real numbers, X a metric space with metric d and XT the set of al...
AbstractLet X be a metric space with metric d, c(X) denote the family of all nonempty compact subset...
AbstractGiven a=(a1,…,an), b=(b1,…,bn)∈Rn with a<b componentwise and a map f from the rectangle Iab=...
Let $\emptyset\neq T \subset \RB, \hspace{.1in} (X,d,+)$ be an additive commutative semigroup with m...
Let $T$ be a nonempty subset of $\RB$, $X$ a metric space with metric $d$ and $X^T$ the set of all f...
AbstractUsing the ‘multiplied’ version of Helly's theorem given by Bárány (Discrete Math. 40 (1982) ...
In this note we consider oscillation of regulated functions. We improve and simplify the proof of th...
Let USCp ⋆(X) be the topological space of real upper semicontinuous bounded functions defined on X w...
contains corrections with respect to published version.We provide a simple proof of a result which g...
For a Tychonoff space X, Cp(X) is the space of all real-valued continuous functions with the topolog...
summary:We compare a recent selection theorem given by Chistyakov using the notion of modulus of var...
AbstractWe prove that certain classes of sequences of positive real numbers satisfy some selection p...
summary:We introduce the spaces $M^{1}_{Y,\varphi }$, $M^{o,n}_{Y,\varphi }$, $\tilde{M}^{o}_{Y,\var...
AbstractWe prove a continuous selection theorem for quasi-lower semicontinuous mappings with values ...
Let H be a Hilbert space. Let ...