Related papers: Precompact Apartness Spaces
Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was…
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…
New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…
We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…
Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to…
It is known that if any function acting from precompact metric space to itself increases the distance between some pair of points then it must decrease distance between some other pair of points. We show that this is not the case for…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
As the use of machine learning models has increased, numerous studies have aimed to enhance fairness. However, research on the intersection of fairness and explainability remains insufficient, leading to potential issues in gaining the…
Cocompactness is a property of embeddings between two Banach spaces, similar to but weaker than compactness, defined relative to some non-compact group of bijective isometries. In presence of a cocompact embedding, bounded sequences (in the…
How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may…
The Baire category theorem states that every complete pseudometric space is a Baire space. There are some results in metric spaces which have their analogue in uniform spaces, however this is not one of them. Nonetheless, since the Baire…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
The definition of accessible coherence is proposed. Through local measurement on the other subsystem and one way classical communication, a subsystem can access more coherence than the coherence of its density matrix. Based on the local…