Finally, we investigate the relationships between $\partial$-connected object and (strongly) connected object in the topological category of proximity space.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, an explicit characterization of the separation properties $ST_2$, $\Delta T_2$, $ST_{3}$, $ \Delta T_{3} $ and Tychonoff objects are given in the topological category of proximity space.
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Key Findings & Data:Moreover, we investigate the relationships among $ST_2$, $\Delta T_2$, $ST_{3}$, $ \Delta T_{3} $, the separation properties at a point $p$, the generalized separation properties $T_{i}$, $i=0,1,2$, $\mathbf{T_{0}}$, $\mathbf{T_{1}}$, $\mathbf{T_{2}}$ and Tychonoff objects in this category.
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Conclusion & Impact:Finally, we investigate the relationships between $\partial$-connected object and (strongly) connected object in the topological category of proximity space.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:topological category · proximity space · separation
Abstract
In this paper, an explicit characterization of the separation properties $ST_2$, $\Delta T_2$, $ST_{3}$, $ \Delta T_{3} $ and Tychonoff objects are given in the topological category of proximity space. Furthermore, the (strongly) compact object and $\partial$-connected object are also characterized in the category of proximity space. Moreover, we investigate the relationships among $ST_2$, $\Delta T_2$, $ST_{3}$, $ \Delta T_{3} $, the separation properties at a point $p$, the generalized separation properties $T_{i}$, $i=0,1,2$, $\mathbf{T_{0}}$, $\mathbf{T_{1}}$, $\mathbf{T_{2}}$ and Tychonoff objects in this category. Finally, we investigate the relationships between $\partial$-connected object and (strongly) connected object in the topological category of proximity space.
KULA, M. (2019). ST2, ∆T2, ST3, ∆T3, Tychonoff, compact and ∂-connected objects in the category of proximity spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 2, 490–500. https://ajindex.com/articles/669385
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