On separability criteria for continuous Bitopological spaces

O. Ogola, N. B. Okelo, O. Ongati
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引用次数: 0

Abstract

In this paper, we give characterizations of separation criteria for bitopological spaces via \(ij\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \((X, \tau_{1}, \tau_{2})\) be a \(T_{0}\) space then, the property of \(T_{0}\) is topological and hereditary. Similarly, when \((X, \tau_{1}, \tau_{2})\) is a \(T_{1}\) space then the property of \(T_{1}\) is topological and hereditary. Next, we show that separation axiom \(T_{0}\) implies separation axiom \(T_{1}\) which also implies separation axiom \(T_{2}\) and the converse is true.
连续双拓扑空间的可分性准则
本文通过\(ij\) -连续性给出了双拓扑空间分离准则的刻画。我们证明了如果一个双拓扑空间是一个分离公理空间,那么该分离公理空间同时具有拓扑和遗传性质。例如,设\((X, \tau_{1}, \tau_{2})\)是一个\(T_{0}\)空间,\(T_{0}\)的性质是拓扑的和遗传的。同样,当\((X, \tau_{1}, \tau_{2})\)是\(T_{1}\)空间时,\(T_{1}\)的性质是拓扑的和遗传的。接下来,我们证明分离公理\(T_{0}\)隐含分离公理\(T_{1}\),分离公理也隐含分离公理\(T_{2}\),反之为真。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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10
审稿时长
8 weeks
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