Szuca, Piotr Every almost continuous function is polygonally almost continuous. (English) Zbl 1035.26005 Real Anal. Exch. 25(1999-2000), No. 2, 691-694 (2000). A function \(f: \mathbb{I} \rightarrow \mathbb{R}\) is almost continuous (AC) if whenever \(U\subset \mathbb{I} \times \mathbb{R}\) is an open set containing the graph of \(f\), then \(U\) contains the graph of a continuous function.A function \(f: \mathbb{I} \rightarrow \mathbb{R}\) is polygonally almost continuous (PAC) if whenever \(U\subset \mathbb{I} \times \mathbb{R}\) is an open set containing the graph of \(f\), then \(U\) contains the graph of a picewise linear continuous function with all vertices of \(f\). The main result of this paper: Every AC function \(f: \mathbb{I} \rightarrow \mathbb{R}\) is PAC. Reviewer: Ryszard Pawlak (Łódź) MSC: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable Keywords:Darboux functions; almost continuous functions; polygonally almost continuous functions × Cite Format Result Cite Review PDF