Topology on grill-filter space and continuity

Modak, Shyamapada

doi:10.5269/bspm.v31i2.16603

Cited by 11 publications

(7 citation statements)

References 12 publications

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“…Kuratowski defined and studied the idea of ideal from filter [16]. Also, this notion has been studied by many topologists in different directions in [11,12]. The notion of ideal comes across as the dual structure of filter.…”

Section: Introductionmentioning

confidence: 99%

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On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

ÖZKOÇ,

KÖSTEL

2024

Preprint

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The main purpose of this paper is to introduce and study two new operators $(\cdot)_{R}^{\diamond}$ and $cl_{R}^{\diamond}(\cdot)$ via primal which is a new notion. We also show that the operator $cl_{R}^{\diamond}(\cdot)$ is a Kuratowski closure operator, while the operator $(\cdot)_{R}^{\diamond}$ is not. In addition, we prove that the topology on $X$, shown as $\tau_{R}^{\diamond}$, obtained by means of the operator $cl_{R}^{\diamond}(\cdot)$ is finer than $\tau_{\delta}$, where $\tau_{\delta}$ is the family of $\delta$-open subsets of a space $(X,\tau)$. Moreover, we not only obtain a base for the topology $\tau_{R}^{\diamond}$ but also prove many fundamental results concerning this new structure. Furthermore, we give many counterexamples related to our results. 2020 AMS Classifications: 54A05; 54B99; 54C60.

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Section: Introductionmentioning

confidence: 99%

“…Also, the other classical structure of general topology in the literature is the notion of grill. It was introduced by Choquet [15] in 1947 and studied by many authors in [6,7,8,9,10,11,12,13,14]. Recently, Acharjee et al introduced a new classical structure called primal [1].…”

Section: Introductionmentioning

confidence: 99%

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

ÖZKOÇ,

KÖSTEL

2024

Preprint

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“…Moreover, all θ-open sets form a topology on G that is coarser than τ and is denoted by τ θ . More fundamental properties of primal spaces and primal soft topological spaces were introduced in [7,8,[11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Primal Structure with Closure Operators and Their Applications

Al-Omari,

Alqahtani

2023

Mathematics

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Acharjee et al. have created a new structure in mathematics called a primal. Therefore, the primary goal of this research was to introduce and explore more primal space features. Additionally, we studied some of the fundamental characteristics of two novel operators that we define using primal spaces. Using these new operators, we were able to create a weaker version of the original topology. Finally, we provide some examples to further illustrate our discussion of some of their characteristics.

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“…The generalization of connectedness has been defined in [18,26] More features of connectedness types given in [20] were examined in [14]. In addition, many operators such as local closure function [1], semi-closure local function [9] , weak semi-local function [35,36], semi-local function [13], a-local function [2,21], M-local function [22], c * -local function [29], Ω-operator [19] and ψ * -operator [23] are defined in recent years. In this study, we define new types of connectedness by using local functions and local closure functions.…”

Section: Introductionmentioning

confidence: 99%

New types of connectedness and intermediate value theorem in ideal topological spaces

Yalaz

Kaymakci

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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The definitions of new type separated subsets are given in ideal topological spaces. By using these definitions, we introduce new types of connectedness. It is shown that these new types of connectedness are more general than some previously defined concepts of connectedness in ideal topological spaces. The new types of connectedness are compared with well-known connectedness in point-set topology. Then, the intermediate value theorem for ideal topological spaces is given. Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.

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Topology on grill-filter space and continuity

Abstract: This paper will discuss about a new topology, obtained from a grill and a filter on the same set. The Characterizations and open base of the new topology are also aim of this paper. The generalized continuity is also a part of this paper.

Cited by 11 publications

References 12 publications

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

Primal Structure with Closure Operators and Their Applications

New types of connectedness and intermediate value theorem in ideal topological spaces

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