Discontinuous Functions as Limits of Compactly Supported Formulas

A bounded real valued function with domain R and one point of discontinuity can be discontinuous in six ways. In beginning textbooks such functions are usually defined piecewise with each piece being given by a formula. Here we give six examples, each having a different type of discontinuity at its...

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Bibliographic Details
Published in:The College mathematics journal 2020-11, Vol.51 (5), p.337-344
Main Author: Marshall Ash, J.
Format: Article
Language:English
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MSC: 26A15
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Summary:A bounded real valued function with domain R and one point of discontinuity can be discontinuous in six ways. In beginning textbooks such functions are usually defined piecewise with each piece being given by a formula. Here we give six examples, each having a different type of discontinuity at its unique point of discontinuity. Each example type is represented as a pointwise limit of quite simple continuous functions. Each approximating function can be given by an elementary formula and also can be chosen to be of compact support.
ISSN:0746-8342
1931-1346
DOI:10.1080/07468342.2020.1820284