On compactness and connectedness of the paratingent

Wojciech Zygmunt

Abstract


In this note we shall prove that for a continuous function \(\varphi : \Delta\to\mathbb{R}^n\), where \(\Delta\subset\mathbb{R}\),  the paratingent of \(\varphi\) at \(a\in\Delta\) is a non-empty and compact set in \(\mathbb{R}^n\) if and only if \(\varphi\) satisfies Lipschitz condition in a neighbourhood of \(a\). Moreover, in this case the paratingent is a connected set.

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References


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DOI: http://dx.doi.org/10.17951/a.2016.70.2.91
Date of publication: 2016-12-24 22:42:02
Date of submission: 2016-12-23 22:07:12


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