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Mapping nearly continuous function by Newton-like operators in Baire's space

The paper presents a mapping 𝐹𝑛: 𝑋 → 𝑌, where 𝐹acts on a topological space 𝑋 into a regular topological space 𝑌 that is nearly continuous. We use Newton-like operators in Baire’s space in the presence of singularities of Jacobian matrices with contributory factor of the Tikhonov regularization parameter introduced on the discontinuous system in order to enforce the homeomorphic image to be continuous under the induced closed graph theorem. Keywords: nonlinear system; Baire’s space; Newton-like methods; strange attractor.