Related papers: Creature forcing and topological Ramsey spaces
This paper initiates the study of picture fuzzy topological spaces. In order to develop a mechanism to construct picture fuzzy topological spaces, we prove some basic results related to picture fuzzy sets together with the introduction of…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.
In this paper, we will develop a significantly more general notion of classical Ramsey numbers (extending most other graph-theoretic generalizations) and make some preliminary characterizations of these new Ramsey numbers using simple…
Departing from a suitable categorical concept of topogenous orders defined relative to the bifibration of subobjects, this note introduces and studies topogenous orders on faithful and amnestic functors. Amongst other things, it is shown…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…
In this paper we show that a countable structure admitting a finite monomorphic decomposition has finite big Ramsey degrees if and only if so does every monomorphic part in its minimal monomorphic decomposition. The necessary prerequisite…
A new phenomenological dark energy model, originally associated to the large-scale structure formation and considered as a solution to the fine-tuning and coincidence problems related to the cosmological constant, was analyzed within the…
Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in…
We introduce a class of learning problems where the agent is presented with a series of tasks. Intuitively, if there is relation among those tasks, then the information gained during execution of one task has value for the execution of…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We consider classes T of topological spaces (referred to as T-spaces) that are stable under continuous images and frequently under arbitrary products. A local T-space has for each point a neighborhood base consisting of subsets that are…
I will give a presentation of an abstract approach to finite Ramsey theory found in an earlier paper of mine. I will prove from it a common generalization of Deuber's Ramsey theorem for regular trees and a recent Ramsey theorem of Jasinski…
All biological and artificial agents must learn and make decisions given limits on their ability to process information. As such, a general theory of adaptive behavior should be able to account for the complex interactions between an…
We systematically investigate morphisms and equivalences of toposes from multiple points of view. We establish a dual adjunction between morphisms and comorphisms of sites, introduce the notion of weak morphism of toposes and characterize…
For $f,g\in\omega\ho$ let $\mycfa_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e. for every branch $\nu$ of the $f$-tree, one of the $g$-trees contains $\nu$. $\myc_{f,g}$ is…
We introduce the notion of a $\theta$-almost twisted Poisson structure on manifolds, which involves incorporating a closed $1$-form $\theta$ into twisted Poisson structures under specific conditions. We provide a characterization of this…
There are relatively few conventions followed in reinforcement learning (RL) environments to structure the action spaces. As a consequence the application of RL algorithms to tasks with large action spaces with multiple components require…
Ramsey theory is the study of conditions under which mathematical objects show order when partitioned. Ramsey theory on the integers concerns itself with partitions of $[1,n]$ into $r$ subsets and asks the question whether one (or more) of…