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Weakly symmetric functions and weakly symmetrically continuous functions. (English) Zbl 1384.26018

Although the existence of a nowhere weakly symmetrically continuous function \(f : {\mathbb R}\rightarrow {\mathbb R}\) that is everywhere weakly symmetric, remains open, the author proves that there exists a nowhere weakly symmetric function \(f : {\mathbb R}\rightarrow {\mathbb R}\) that is everywhere weakly symmetrically continuous and everywhere weakly continuous.

MSC:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A21 Classification of real functions; Baire classification of sets and functions
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