Related papers: Transfunctions
Generalized sine and cosine functions, $\sin_{n}$ and $\cos_{n}$, that parametrize the generalized unit circle $x^n+y^n=1$ are, much like their classical circular counterparts, extendable as complex analytic functions. In this article, we…
A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact…
In the paper, it is given isomorphic classification of $F$-spaces of $log$-integrable measurable functions constructed using different measure spaces. At the same time, it is proved that such spaces are non-isometric.
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are…
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…
Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.
For a measurable space ($X,\mathcal{A}$), let $\mathcal{M}(X,\mathcal{A})$ be the corresponding ring of all real valued measurable functions and let $\mu$ be a measure on ($X,\mathcal{A}$). In this paper, we generalize the so-called…
How can one lift a functional defined on maps from a space X to a space Y into a functional defined on maps from X into P(Y) the space of probability distributions over Y? Looking at measure-valued maps can be interpreted as knowing a…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
An ordinal-valued metric taking its values in the set of all countable ordinals can be assigned to a metrizable set of nodes in a transfinite graph. Then, a variety of results concerning nodal eccentricities, radii, diameters, centers,…
$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic…
The cross topology $\gamma$ on a product of topological spaces $X$ and $Y$ is the collection of all sets $G\subseteq X\times Y$ such that the intersection of $G$ with every vertical line and every horizontal line is an open subset of either…
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.
It is proved that the random integral mappings (some type of functionals of L\'evy processes) are always isomorphisms between convolution semigroups of infinitely divisible measures. However, the inverse mappings are no longer of the random…
In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces $A$ and $B$ of $C_0(X,E)$ and $C_0(Y,F)$ where $X$ and $Y$ are locally compact Hausdorff spaces and $E$ and $F$ are normed…
This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…
A graph is called (edge)-SIT if for some probability measure on paths, the number of mutual edges in two independent paths has finite mean. We show that transience is equivalent to the property of (edge)-SIT.
Clearly, a generalized inverse limit of metrizable spaces indexed by $\mathbb N$ is metrizable, as it is a subspace of a countable product of metrizable spaces. The authors previously showed that all idempotent, upper semi-continuous,…