Abstract
Let \( \mathcal{T}_\psi \) be a ψ-density topology for a fixed function ψ. This paper is concerned with the family of ψ-continuous functions, that means continuous functions from (ℝ, \( \mathcal{T}_\psi \)) into (ℝ, \( \mathcal{T}_\psi \)). The family of such functions forms a lattice and is not closed under addition and uniform convergence. There exist functions ψ for which even linear functions are not ψ-continuous.
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Filipczak, M., Terepeta, M. ψ-continuous functions. Rend. Circ. Mat. Palermo 58, 245–255 (2009). https://doi.org/10.1007/s12215-009-0018-y
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DOI: https://doi.org/10.1007/s12215-009-0018-y