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.
topological category proximity space separation closedness connectedness compact objects
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 1 Nisan 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 48 Sayı: 2 |