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of 552
pro vyhledávání: '"54a05"'
In the work "Generalized approximation spaces generation from $\mathbb{I}_{j}$-neighborhoods and ideals with application to Chikungunya disease, published in \emph{AIMS Mathematics}, \textbf{9}(4) (2024), 10050$-$10077," Al-Shami and Hosny introduced
Externí odkaz:
http://arxiv.org/abs/2412.05284
We prove analogues of classical results for higher homotopy groups and singular homology groups of pseudotopological spaces. Pseudotopological spaces are a generalization of (\v{C}ech) closure spaces which are in turn a generalization of topological
Externí odkaz:
http://arxiv.org/abs/2409.01370
Publikováno v:
Topology and its Applications, 358:109113, 2024
We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm $*$ on the unit interval $[0,1]$. Let $k^*$ be the supremum of the idempotent elements of $*$ in $[0,1)$. It is shown that if $k^*=1$ (resp. $
Externí odkaz:
http://arxiv.org/abs/2408.07548
Autor:
İzci, Bilge, Özkoç, Murad
The aim of this paper is to introduce the notion of $a$-locally closed set by utilizing $a$-open sets defined by Ekici and to study some properties of this new notion. Also, some characterizations and many fundamental results regarding this new conce
Externí odkaz:
http://arxiv.org/abs/2408.03169
Autor:
Issaka, Faical Yacine, Özkoç, Murad
The main purpose of this paper is to introduce and study minimal and maximal ideals defined on ideal topological spaces. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of $2^X$, where $2^X$ is the powe
Externí odkaz:
http://arxiv.org/abs/2407.17612
Autor:
Lipparini, Paolo
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence, hence equiv
Externí odkaz:
http://arxiv.org/abs/2407.08446
Autor:
Guerrero, Pablo Andújar
We show that separability and second-countability are first-order properties among topological spaces definable in o-minimal expansions of $(\mathbb{R},<)$. We do so by introducing first-order characterizations -- definable separability and definable
Externí odkaz:
http://arxiv.org/abs/2405.07114
Autor:
Guerrero, Pablo Andújar
We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of de
Externí odkaz:
http://arxiv.org/abs/2405.07112
Autor:
Valent, Tullio
Two approaches to Lipschitz structures for any set are presented, studied and compared. The first approach is similar to the one proposed in Fraser, Jr. R. B., Axiom systems for Lipschitz structures, Fundamenta Mathematicae, (1970), where Lipschitz s
Externí odkaz:
http://arxiv.org/abs/2404.14026
Autor:
Richmond, Tom, Wajch, Eliza
A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in $\mathbf{ZF}$ a new characterization of iso-dense spaces in terms of special quasior
Externí odkaz:
http://arxiv.org/abs/2404.06623