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Generalizations of connected and compact sets by \(d_\delta\)-closure operator. (English) Zbl 1423.54045

Summary: In this paper, we introduce two new concepts, namely, a subset being \(d_\delta\)-connected relative to a topological space, and a subset being \(D_\delta\)-closed relative to the space. The former is a generalization of the concept of a subset being \(\theta\)-connected relative to a space, and the latter is analogous to the \(H(i)\) space.

MSC:

54D05 Connected and locally connected spaces (general aspects)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54C08 Weak and generalized continuity
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