Topological Neighborhood Induced Ideal Convergence of Sequences of Sets
Keywords:
ideal convergence, sequence of sets, neighborhood convergenceAbstract
This paper investigates the concept of ideal convergence of sequences of sets through neighborhoods in topological context. The operators ∆−x and ∆+x are employed as fundamental tools for the establishment of nI-limit inferior and nI-limit superior. For sequence of sets, ‘sandwich’ theorem like description is presented under nI-convergence. Several inclusion properties of nI − lim inf, nI − lim sup and related notions are derived. It has been shown that in an I compact space, sequence of closed sets having I-intersection property always possess nI − lim inf. The scope and limitations of the theory are further tracked down through counterexamples.
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