In this article a new property which is namely, δ — βc — connectedness in Topological spaces is introduced and investigated by utilizing new generalized of open set which is called δ — βc — open set. Several characterizations and fundamental properties concerning of this class of connectedness are obtained. Moreover, the relationships between this class of connectedness and various other weaker and stronger forms of connectedness are discussed. The behavior of δ — βc — Connected space with respect to some denominations of well-known mappings is studied. Further the components of δ — βc — connectedness and its properties are considered. Mathematics Subject Classification: Primary: 54A05; Secondary: 54D05.

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