A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of ...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof(κ) carries a partial square. A famous theorem in set theory is the result that the failure of the square principle κ, for a regular uncountable cardinal κ, is equiconsistent with a Mahlo cardinal. Solovay p...

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to bounded linear operator $\widehat {f} \mathcal {F}(M) {F}(N)$ their corresponding Lipschitz-free spaces. In this paper, we give necessary and sufficient condition for {f}$ compact terms of conditions on $f$ . This extends result by A. Jiménez-Vargas M. Villegas-Vallecillos the case non-separable...

In this note, we provide a new proof of Magidor's theorem that the least strongly compact cardinal can be the least supercompact cardinal. A classical theorem of Magidor [5] states that it is consistent, relative to the existence of a supercompact cardinal, for the least supercompact cardinal to be the least strongly compact cardinal. There are currently two different proofs of this fact—the or...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

Abstract We prove that it is consistent Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on $\omega _2$ , thereby contributing to study of tension between compactness incompactness in set theory. The poset which produces final model follows collapse an ineffable cardinal first with iteration club adding (with anticipation) second specializing trees. In part...