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Abstract A function f: ℝ → ℝ is internally cliquish (internally quasi-continuous) if it is cliquish (quasi-continuous) and the set of discontinuity points of f is nowhere dense. We prove… Click to show full abstract
Abstract A function f: ℝ → ℝ is internally cliquish (internally quasi-continuous) if it is cliquish (quasi-continuous) and the set of discontinuity points of f is nowhere dense. We prove that the set of internally cliquish (internally quasi-continuous) functions is dense and σ-strongly porous set in the family of cliquish (quasi-continuous) functions. The analogous result is obtained also for the family of functions having the Świątkowski property.
Keywords:
dense porous;
porous subsets;
subsets families;
quasi continuous;
functions dense;
families cliquish
Journal Title: Quaestiones Mathematicae
Year Published: 2019
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Journal Title: Quaestiones Mathematicae
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!