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ALMOST $\Omega$-BOUNDEDNESS IN $L$-TOPOLOGICAL SPACE
Keywords:
molecules, $R$-neighborhoods, $L$-topological space, limit and $\theta$-cluster points, $\Omega$-nets, constant $\alpha$-nets, $\alpha$-filters, $\alpha$-ideals, almost $\Omega$-compact, almost $\Omega$-bounded sets.DOI:
https://doi.org/10.17654/0972087124012Abstract
In this paper, we introduce and study the notion of almost $\Omega$-boundedness on arbitrary $L$-sets in $L$-topological spaces by using the notion of $\theta$-upper limit of $\Omega$-nets. Several characterizations of almost $\Omega$-boundedness in terms of convergence of constant $\alpha$-nets and $\alpha$-ideals are obtained. We prove that the notion is a good extension, productive and topologically invariant.
Received: February 18, 2024
Accepted: April 4, 2024`
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