Multiset proximity spaces

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• 作者：A. Kandil^a ; ^{dr.ali_kandil@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; O.A. Tantawy^b ; ^{drosamat@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; S.A. El-Sheikh^c ; ^{elsheikh33@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Amr Zakaria ; ^c ; ^{amr.zakaria@edu.asu.edu.eg" class="auth_mail" title="E-mail the corresponding author} ; ^{amr_zakaria2008@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multiset topologies ; Multiset proximity ; T4-multiset space ; Compact multiset ; Multiset δ-δ- neighborhood ; Semi-compatible
• 刊名：Journal of the Egyptian Mathematical Society
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：24
• 期：4
• 页码：562-567
• 全文大小：400 K

文摘

A multiset is a collection of objects in which repetition of elements is essential. This paper is an attempt to explore the theoretical aspects of multiset by extending the notions of compact, proximity relation and proximal neighborhood to the multiset context. Examples of new multiset topologies, open multiset cover, compact multiset and many identities involving the concept of multiset have been introduced. Further, an integral examples of multiset proximity relations are obtained. A multiset topology induced by a multiset proximity relation on a multiset M   has been presented. Also the concept of multiset rieve&_eid=1-s2.0-S1110256X16000134&_mathId=si1.gif&_user=111111111&_pii=S1110256X16000134&_rdoc=1&_issn=1110256X&md5=f20c0c6b7bfe3a1edb869c9610e6946f" title="Click to view the MathML source">δ-$\delta \text{-}$ neighborhood in the multiset proximity space which furnishes an alternative approach to the study of multiset proximity spaces has been mentioned. Finally, some results on this new approach have been obtained and one of the most important results is: every rieve&_eid=1-s2.0-S1110256X16000134&_mathId=si2.gif&_user=111111111&_pii=S1110256X16000134&_rdoc=1&_issn=1110256X&md5=8110d1a0ce22dad58f7d8374a6304af9" title="Click to view the MathML source">T₄-$T_4\text{-}$ multiset space is semi-compatible with multiset proximity relation δ on M ( Theorem 5.10).