Related papers: Generic non-extendability and total unboundedness …

We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…

We consider generalizations of classical function spaces by requiring that a holomorphic in ${\Omega}$ function satisfies some property when we approach from ${\Omega}$, not the whole boundary, but only a part of it. These spaces endowed…

In this paper we prove generic results concerning Hardy spaces in one or several complex variables. More precisely, we show that the generic function in certain Hardy type spaces is totally unbounded and hence non-extentable, despite the…

We give examples of $L^{1}$-functions that are essentially unbounded on every nonempty open subset of their domains of definition. We obtain such functions as limits of weighted sums of functions with the unboundedly increasing number of…

Let $\Omega$ be a bounded domain in $\mathbb{C}$ such that $\partial \Omega$ does not contain isolated points. Let $R(\Omega)$ be the space of uniform limits on $\overline{\Omega}$ of rational functions with poles off $\overline{\Omega}$,…

The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…

It is shown that the extension of $\R$ by a generic smooth function restricted to the unit cube is o-minimal. The generalization to countably many generic smooth functions is indicated. Possible applications are sketched.

We show topological genericity for the set of functions in the space X, where X denotes the intersection of the Hardy spaces H^p with p<1, on the open unit disc such that the sequence of Taylor coefficients of the function and of all…

Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…

With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…

We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set.

This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks…

We compare possibilities of extension of bounded and unbounded Baire-one functions from subspaces of topological spaces.

In many textbooks on Generalized Functions and Distributions, we can find an example of infinitely differentiable function of bounded support from space D, called a bump function. This example is incorrect since this function is not…

We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…

The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em…

In this article we prove a general result which in particular suggests that, on a simply connected domain in C, all the derivatives and anti-derivatives of the generic holomorphic function are unbounded. A similar result holds for the…

We investigate several boundedness properties of function spaces considered as uniform spaces.

It is known that for $X$ a nowhere locally compact metric space, the set of bounded continuous, nowhere locally uniformly continuous real-valued functions on $X$ contains a dense $G_\delta$ set in the space $C_b(X)$ of all bounded…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…