我们能从一个函数的图形中认出它吗?

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-30 DOI:10.4171/zaa/1730

Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka

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引用次数: 0

摘要

我们分析度量空间上实函数的解析性质与图的拓扑性质之间的“相互作用”。特别地，我们研究了具有闭图、紧图、连通图、路径连通图和局部连通图的函数，并给出了图上等价于函数连续性的9个条件。主要的重点放在例子和反例子上，这些例子说明了我们的假设是多么重要，以及充分条件离必要条件有多远。

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Can one recognize a function from its graph?

\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.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.