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Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence. We also establish basic…
A four-term recurrence relation for squared spherical Bessel functions is shown to yield closed-form expressions for several types of finite weighted sums of these functions. The resulting sum rules, which may contain an arbitrarily large…
We solve a problem on a construction of a separately continuous mapping with the given diagonal, which is the pointwise limit of a sequence of continuous mappings valued in an equiconnected space. We construct an example of a closed-valued…
A person is given a numbered sequence of positions on a sheet of paper. The person is asked, "Which will be the next (or the next after that) position?" Everyone has an opinion as to how he or she would proceed. There are regular sequences…
The class of spaces such that their product with every Lindel\"of space is Lindel\"of is not well-understood. We prove a number of new results concerning such productively Lindel\"of spaces with some extra property, mainly assuming the…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…
The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…
The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
A function from Baire space to the natural numbers is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working…
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate…
A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Spherically complete ball spaces provide a framework for the proof of generic fixed point theorems. For the purpose of their application it is important to have methods for the construction of new spherically complete ball spaces from given…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…