New topologies from obtained operators via weak semi-local function and some comparisons

Yalaz, Ferit; Kaymakci, Aynur Keskin

doi:10.2298/fil2115073y

Cited by 3 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Homeomorphisms in the topological spaces also play a remarkable role for the studying of minimal -open sets. The above ideas will also be introduced in terms of the recent topology introduced by Tormet, Yavina and Brown in [9] and topologies and introduced by Yalaz and Kaymakci in [10].…”

Section: Introductionmentioning

confidence: 99%

Role Of ψ-Operator in the Study of Minimal Open Sets

MIAH,

MODAK,

ISLAM

2023

Iraqi Journal of Science

View full text Add to dashboard Cite

The operator ψ has been introduced as an associated set-valued set function. Although it has importance for the study of minimal open sets as well as minimal I-open sets. As a result of this study, we introduce minimal I^*-open sets . In this study, several characterizations of minimal I^*-open sets are also investigated. This study also discusses the role of minimal I^*-open sets in the *-locally finite spaces. In an aspect of topological invariant, the homeomorphic images of minimal I^*-open set has been discussed here.

show abstract

A new local function and a new compatibility type in ideal topological spaces

Yalaz¹,

Kaymakci²

2023

MATH

View full text Add to dashboard Cite

<abstract><p>In this study, a $ \zeta^*_\Gamma $-local function is defined and its properties are examined. This newly defined local function is compared with the well-known local function and the local closure function according to the relation of being a subset. With the help of this new local function, the $ \Psi_{\zeta^*_\Gamma} $ operator is defined and topologies are obtained. Moreover, alternative answers are given to an open question found in the literature. $ \Psi_{\zeta^*_\Gamma} $-compatibility is defined and its properties are examined. $ \Psi_{\zeta^*_\Gamma} $-compatibility is characterized with the help of the new operator. Finally, new spaces were defined and characterized.</p></abstract>

show abstract

New topologies from obtained operators via weak semi-local function and some comparisons

Cited by 3 publications

References 13 publications

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

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

Role Of ψ-Operator in the Study of Minimal Open Sets

A new local function and a new compatibility type in ideal topological spaces

Contact Info

Product

Resources

About