Abstract
Two problems related to the characterization of continuity are discussed. In the first problem “\(f\) is almost continuous in the sense of Stallings” will be replaced with a weaker condition “\(f\) is a Darboux function” and it will be shown that the characterization of continuity remains true. Also it follows that for the classes of functions considered, “\(f\) is a Darboux function” is the weakest possible condition for which the characterization remains true. In the second problem “\(f\) is almost continuous in the sense of Stallings” will be replaced with a stronger condition “\(f\) is an extendable function”. Then it will be shown that this condition and conditions (2) and (3) are not redundant.
Citation
Richard G. Gibson. "Concerning a characterization of continuity." Real Anal. Exchange 22 (1) 437 - 442, 1996/1997.
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