Author
Listed:
- Murad Özkoç
- Faical Yacine Issaka
- Tareq M. Al-shami
- Anwar J. Fawakhreh
Abstract
In topology, connectedness provides insight into how a space is “in one piece,†rather than being split into disjoint parts. Its significance can be seen through its various applications, such as understanding the nature of solutions to differential equations, the intermediate value theorem, and attaining a maximum and minimum for continuous real-valued functions. Therefore, in this manuscript, we introduce three types of connectedness within the framework of primal topological spaces: u-connectedness, ⋄-connectedness, and Ω-connectedness. The new types introduced provide new categories for topological spaces and help to set up fresh forms of connected components. Through the content, we prove the classes of u-connected spaces, ⋄-connected spaces, and Ω-connected spaces include the class of connected spaces in general topology. Some characterizations of these classes are derived, and interesting results regarding them are presented. With the help of illustrative examples, we examine the conditions guaranteeing the equivalence between the introduced concepts and their classical counterparts. Also, we define the notion of ⋄-separated sets and investigate some of its fundamental properties. Finally, we design a roadmap for future studies, outlining two methods for applying primals to generate rough set models through the hybridization of them with neighborhood systems.
Suggested Citation
Murad Özkoç & Faical Yacine Issaka & Tareq M. Al-shami & Anwar J. Fawakhreh, 2025.
"Connectedness via Primal Topological Spaces With Applications of Primals to Rough Operators,"
Journal of Mathematics, Hindawi, vol. 2025, pages 1-12, September.
Handle:
RePEc:hin:jjmath:3487928
DOI: 10.1155/jom/3487928
Download full text from publisher
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jjmath:3487928. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.