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Smooth Biproximity Spaces and 𝑃-Smooth Quasi-Proximity Spaces
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نویسنده
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Tantawy O. A. ,El-Sheikh S. A. ,Majeed R. A.
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منبع
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Journal Of Linear And Topological Algebra - 2017 - دوره : 6 - شماره : 2 - صفحه:91 -107
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چکیده
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The notion of smooth biproximity space (𝑋, δ1, δ2) where δ1, δ2 are gradation proximities defined by ghanim et al. [10]. in this paper, we show every smooth biproximity space (𝑋, δ1, δ2) induces a supra smooth proximity space δ12 finer than δ1 and δ2. we study the relationship between (𝑋, δ12) and the 𝐹𝑃*-separation axioms which had been introduced by ramadan et al. [23]. furthermore, we show for each smooth bitopological space which is 𝐹𝑃*-𝑇4, the associated supra smooth topological space is a smooth supra proximal. the notion of 𝐹𝑃-(resp. 𝐹𝑃*-) proximity map are also introduced. in addition, we introduce the concept of p-smooth quasi-proximity spaces and prove that the associated smooth bitopological space (𝑋, τδ, τδ−1 ) satisfies 𝐹𝑃-separation axioms in sense of ramadan et al. [10]
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کلیدواژه
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Smooth Bitopological Space ,Supra Smooth Proximity ,Smooth Quasi-Proximity ,𝐹𝑃-Separation Axioms ,Compatibility ,𝐹𝑃-Proximity Map
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آدرس
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Zagaziq University, Faculty Of Science, Department Of Mathematics, Egypt, Ain Shams University, Faculty Of Education, Department Of Mathematics, Egypt, Ain Shams University, Faculty Of Science, Department Of Mathematics, Iraq
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پست الکترونیکی
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rashanm6@gmail.com
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Authors
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