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We are going to widen the scope of the previously defined Hausdorff-integral in two ways. First, in the sense, that we develop the theory of the integral on some naturally generalized measure spaces. Second, we extend it to functions taking…
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…
We study the continuous solutions of several classical functional equations by using the properties of the spaces of continuous functions which are invariant under some elementary linear trans-formations. Concretely, we use that the sets of…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $\mathbb{R}^n$. The degree of compactness will be measured in terms of related entropy numbers. We are more…
Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences with the case of continuous trace $C^*$-algebras. At the level of the spectrum, this translates to only assuming…
In this paper we consider the problem of characterization of topological spaces that embed into countably compact Hausdorff spaces. We study the separation axioms of subspaces of countably compact Hausdorff spaces and construct an example…
The category of compact Hausdorff spaces is the base of tripos. As such it can be freely completed to an elementary topos.
This thesis is divided into two parts. The first one is composed of recollections on operad theory, model categories, simplicial homotopy theory, rational homotopy theory, Maurer-Cartan spaces, and deformation theory. The second part deals…
In this paper, the continuity and strong continuity in domain-free information algebras and labeled information algebras are introduced respectively. A more general concept of continuous function which is defined between two domain-free…
In this paper, we consider a subclass of starlike functions associated with a vertical strip domain. Several results concerned with integral representations, convolutions, and coefficient inequalities for functions belonging to this class…
We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other…
We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.
We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case…
We study compact spaces which are obtained from metric compacta by iterating the operation of inverse limit of continuous sequences of retractions. We denote this class by R. Allowing continuous images in the definition of class R, one…
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…
Much recent work in cardinal characteristics has focused on generalizing results about $\omega$ to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$…
A common feature of many duality results is that the involved equivalence functors are liftings of hom-functors into the two-element space resp. lattice. Due to this fact, we can only expect dualities for categories cogenerated by the…
In this paper we introduce and study so-called $k^*$-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By…