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\((\alpha,\beta,\theta,\partial,{\mathcal I})\)-continuous mappings and their decomposition. (English) Zbl 1098.54509
Summary: We introduce the concept of \((\alpha,\beta,\theta,\partial,{\mathcal I})\)-continuous mappings and prove that if \(\alpha,\beta\) are operators on the topological space \((X,\tau)\) and \(\theta,\theta^*\), \(\partial\) are operators on the topological space \((Y,\varphi)\) and \({\mathcal I}\) a proper ideal on \(X\), then a function \(f:X \to Y\) is \((\alpha,\beta,\theta\wedge \theta^*,\partial,{\mathcal I})\)-continuous if and only if it is both \((\alpha, \beta,\theta,\partial,{\mathcal I})\)-continuous and \((\alpha,\beta,\theta^*, \partial,{\mathcal I})\)-continuous, generalizing a result of J. Tong. Additional results on \((\alpha,Int,\theta,\partial,\{\emptyset\})\)-continuous maps are given.

MSC:
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54C05 Continuous maps
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