Can one recognize a function from its graph?
Jürgen Appell
Universität Würzburg, GermanyAgnieszka Chlebowicz
Rzeszów University of Technology, PolandSimon Reinwand
TNG Technology Consulting GmbH, Unterföhring, GermanyBeata Rzepka
Rzeszów University of Technology, Poland
Abstract
We analyse the “interplay” between analytical properties of a real function on a metric space, on the one hand, and topological properties of its graph, on the other. In particular, we study functions with closed, compact, connected, pathwise connected, or locally connected graphs, and we give nine conditions on the graph which are equivalent to the continuity of a function. A main emphasis is put on examples and counterexamples which illustrate how significant our hypotheses are, and how far sufficient conditions are from being necessary.
Cite this article
Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka, Can one recognize a function from its graph?. Z. Anal. Anwend. 42 (2023), no. 1/2, pp. 203–233
DOI 10.4171/ZAA/1730