Abstract This paper introduces the notion of a ‘pseudo centre’ of a suitable bounded region in R n . We investigate general properties of a pseudo centre by means of techniques provided by calculus, differential geometry, and topology. While calculus allows to introduce ‘depth diagram’ and relates that to constraint extreme value problems, the topological point of view allows to study the qualitative properties of a pseudo centre. We have discussed the relation of index of a pseudo centre to Lusternik-Schnirelmann category of a space. The paper is concluded by some discussions regarding the generalised version of the problem and further research.

中文翻译：

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伪中心及其应用

摘要 本文介绍了 R n 中合适有界区域的“伪中心”的概念。我们通过微积分、微分几何和拓扑学提供的技术研究伪中心的一般性质。虽然微积分允许引入“深度图”并将其与约束极值问题相关联，但拓扑的观点允许研究伪中心的定性特性。我们已经讨论了伪中心的索引与空间的 Lusternik-Schnirelmann 范畴的关系。该论文的结论是对问题的广义版本和进一步研究进行了一些讨论。