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\(p\)-\(\mathcal J\)-generator and \(p_1\)-\(\mathcal J\)-generator in bitopology. (English) Zbl 1424.54067

Summary: In this article, we investigate several relations between \(p\)-\(\mathcal I\)-generator, \(p_1\)-\(\mathcal I\)-generator with \(p_1\)-Lindelöf and \(p_1\)-Lindelöf spaces by using \(\tau_i\)-codense, \((i, j)\)-meager set, \((i, j)\)-nowhere dense set and perfect mapping of bitopological spaces. Various relations between \(p\)-compactness, \(p\)-Lindelöfness, \(p_1\)-Lindelöfness, topological ideal, \((i, j)\)-meager, \((i, j)\)-Baire space in bitopological spaces are investigated. Some properties are studied by using perfect mappings in product bitopological spaces. It is found that bitopological spaces have many applications in real life.

MSC:

54E55 Bitopologies
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