Pseudo centre and its applications

This paper introduces the notion of a ‘pseudo centre’ of a suitable bounded region in Rn. 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.