相关论文: Recent uses of connectedness in functional analysi…
Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\colon \Omega\to \mathbb{R}$. The focus is on results involving compactness. To this end, a…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
A strict interpretation of connectionism mandates complex networks of simple components. The question here is, is this simplicity to be interpreted in absolute terms? I conjecture that absolute simplicity might not be an essential attribute…
Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening,…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
This paper is divided to two parts. In the first part, we provide elementary proofs for some important results in multi-objective optimization. The given proofs are so simple and short in compared to the existing ones. Also, a Pareto…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…
In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…
Formal concepts and closed itemsets proved to be of big importance for knowledge discovery, both as a tool for concise representation of association rules and a tool for clustering and constructing domain taxonomies and ontologies.…
Since the seminal paper by Tversky and Kahneman, the conjunction fallacy has been the subject of multiple debates and become a fundamental challenge for cognitive theories in decision-making. In this article, we take a rather uncommon…
With the aim of developing the concepts of positive logic and in response to a question that was asked by Poizat in one of his articles, I wrote this article. The main topic is the study of compactness in the extension as a compact…
It is known that, in finite dimensions, the support function of a compact convex set with non empty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper we realize a thorough study of the…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…