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Some generalized continuous maps via ideal. (English) Zbl 1449.54022

Summary: The \(\mu^*\)-open sets are sets where the closure has been considered in topological space and interior in generalized topological space. In this paper, we have studied the properties of \(\mu^*\)-open sets and defined the \(\mu^*\)-continuity in generalized topology on topological space. The \(I_\mu\)-open sets are generalized open sets of \(\mu^*\)-open sets. Some properties of \(I_\mu\)-open sets have been proved and defined the \(I_\mu\)-continuity and weakly \(I_\mu\)-continuity in generalized topology on topological spaces via ideal. Further, we have developed some classical properties on \(\mu^*\)-continuity, \(I_\mu\)-continuity and weakly \(I_\mu\)-continuity.

MSC:

54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54A05 Topological spaces and generalizations (closure spaces, etc.)
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