On preserving continuity in ideal topological spaces
| Autor: | Aleksandar Pavlović, Anika NJamcul |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Georgian Mathematical Journal. 29:567-574 |
| ISSN: | 1572-9176 1072-947X |
| DOI: | 10.1515/gmj-2022-2161 |
| Popis: | Some sufficient conditions are presented for the continuity of the mapping f : ⟨ X , τ X * ⟩ → ⟨ Y , τ Y * ⟩ f\colon\langle X,\tau_{X}^{*}\rangle\to\langle Y,\tau_{Y}^{*}\rangle , where τ X * \tau_{X}^{*} and τ Y * \tau_{Y}^{*} are the topologies induced by the local function on 𝑋 and 𝑌, resp. under the assumption that the mapping from ⟨ X , τ X ⟩ \langle X,\tau_{X}\rangle to ⟨ Y , τ Y ⟩ \langle Y,\tau_{Y}\rangle is continuous. Further, we consider open and closed functions in the cases in which the open (or closed) mapping is preserved through the domain and codomain “idealization”. Through several examples, we illustrate that the considered conditions cannot be weakened. |
| Databáze: | OpenAIRE |
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