Applications of a conditional preopen sets in Bitopological spaces: Topological Space in Mathematics

ISBN 10: 3847300806 / ISBN 13: 9783847300809
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Applications of a conditional preopen sets in Bitopological spaces: Topological Space in Mathematics. N° de ref. de la librería

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Sinopsis: The purpose of the present work is to introduce and investigate a new class of sets called (i, j)-Ps? open sets, and use this class to define and study new concepts in bitopological spaces such as continuity and separation axioms. At the beginning of this work, we define the class of (i, j)-Ps? open sets which contained in the class of j-preopen sets and also contained in the class of (i, j)-gp? open sets. It is shown that the family of (i, j)-Ps? open sets form a supratopology on X. We prove that the family of (i, j)-Ps? open sets and the family of j-preopen sets are identical when (X, ?i) are semi-T1-spaces. Finally, some separation axioms such as T0, T1 and T2 spaces are defined in bitopological spaces, also R0, R1 and Urysohn spaces are defined and the relation between them are found by using the new type of graph functions called (i, j)-Ps ? closed graph. It is noticed that if (X, ?1, ?2) is (i, j)-Ps?Tk, then it is (i, j)-Ps?Tk-1, for k=1, 2. It is proved that a bitopological space (X, ?1, ?2) is (i, j)-Ps?T1 if the (i, j)-Ps? derived set of every point of X is empty.

Biografía del autor: Hardi Nasraddin (7-2-1984) was born in Sulaimania,Kurdistan. After studying Mathematics at the University of Sulaimani, He got it the MSc. degree.Hardi obtain important results in Bitopological spaces, and he has some papers on this field, now he is lecturing in Mathematics Department at University Sulaimani.

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Hardi Nasralddin
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Descripción LAP Lambert Academic Publishing, Germany, 2012. Paperback. Estado de conservación: New. Aufl.. 220 x 150 mm. Language: English . Brand New Book ***** Print on Demand *****.The purpose of the present work is to introduce and investigate a new class of sets called (i, j)-Ps- open sets, and use this class to define and study new concepts in bitopological spaces such as continuity and separation axioms. At the beginning of this work, we define the class of (i, j)-Ps- open sets which contained in the class of j-preopen sets and also contained in the class of (i, j)-gp- open sets. It is shown that the family of (i, j)-Ps- open sets form a supratopology on X. We prove that the family of (i, j)-Ps- open sets and the family of j-preopen sets are identical when (X, i) are semi-T1-spaces. Finally, some separation axioms such as T0, T1 and T2 spaces are defined in bitopological spaces, also R0, R1 and Urysohn spaces are defined and the relation between them are found by using the new type of graph functions called (i, j)-Ps - closed graph. It is noticed that if (X, 1, 2) is (i, j)-Ps-Tk, then it is (i, j)-Ps-Tk-1, for k=1, 2. It is proved that a bitopological space (X, 1, 2) is (i, j)-Ps-T1 if the (i, j)-Ps- derived set of every point of X is empty. Nº de ref. de la librería AAV9783847300809

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Descripción LAP Lambert Academic Publishing. Paperback. Estado de conservación: New. Paperback. 88 pages. Dimensions: 8.7in. x 5.9in. x 0.2in.The purpose of the present work is to introduce and investigate a new class of sets called (i, j)-Ps open sets, and use this class to define and study new concepts in bitopological spaces such as continuity and separation axioms. At the beginning of this work, we define the class of (i, j)-Ps open sets which contained in the class of j-preopen sets and also contained in the class of (i, j)-gp open sets. It is shown that the family of (i, j)-Ps open sets form a supratopology on X. We prove that the family of (i, j)-Ps open sets and the family of j-preopen sets are identical when (X, i) are semi-T1-spaces. Finally, some separation axioms such as T0, T1 and T2 spaces are defined in bitopological spaces, also R0, R1 and Urysohn spaces are defined and the relation between them are found by using the new type of graph functions called (i, j)-Ps closed graph. It is noticed that if (X, 1, 2) is (i, j)-PsTk, then it is (i, j)-PsTk-1, for k1, 2. It is proved that a bitopological space (X, 1, 2) is (i, j)-PsT1 if the (i, j)-Ps derived set of every point of X is empty. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Nº de ref. de la librería 9783847300809

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