Points of weak symmetric continuity. (English) Zbl 0967.26003

The author quotes some known results on sets of points of continuity relative to various notions of continuity as a motivation for his study of points of symmetric continuity. Then he proves in Th. 7: Any set of reals is the set of points of weak symmetric continuity for some function \(f:\mathbb R\rightarrow \mathbb N\).
A function \(f\) constructed in the paper has an infinite range. The proof is based on a technical lemma presented already in 1997 at the Auburn conference and requires the axiom of choice. If the range of such a function is finite and contains not more than 3 points then a point of weak symmetric continuity exists. Some open problems are mentioned.


26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A03 Foundations: limits and generalizations, elementary topology of the line