• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.539-547
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• 2005

The class of b-open sets in the sense of $Andrijevi{\acute{c}}$ ([3]), was discussed by El-Atik ([9]) under the name of ${\gamma}-open$ sets. This class is closed under arbitrary union. The aim of this paper is to use ${\Lambda}-sets$ and ${\vee}-sets$ due to Maki ([15]) some topologies are constructed with the concept of b-open sets. $b-{\Lambda}-sets,\;b-{\vee}-sets$ are the basic concepts introduced and investigated. Moreover, several types of near continuous function based on $b-{\Lambda}-sets,\;b-{\vee}-sets$ are constructed and studied.