Idealization of Some Topological Concepts

B. Al-Nashef and K. Al-Zoubi

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-8

Abstract:

An approach is followed here to generate a new topology on a set 𠑋 from an ideal ℠and a family 𠒮 of subsets of 𠑋 . The so-obtained topology is related to other known topologies on 𠑋 . The cases treated here include the one when 𠒮 = 𠑇 𠛼 is taken, then the case when 𠒮 = 𠑅 𠑂 ( 𠑋 , 𠑇 ) is considered. The approach is open to apply to other choices of 𠒮 . As application, some known results are obtained as corollaries to those results appearing here. In the last part of this work, some ideal-continuity concepts are studied, which originate from some previously known terms and results.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:795106

DOI: 10.1155/2011/795106

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