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The product formula

January 1991
Collectanea Mathematica 42(2)

Authors:

Genaro López Acedo

Universidad de Sevilla

A useful property of the Brouwerdegree relates the degree of a composition of maps to the degree of each map. This property, which can be generalized for the Leray Schauder degree and in some cases for the A-proper maps is called the Product Formula. In a previous paper we developed a generalized degree theory for a class of mappings, this class contains the class of A-proper mappings and compact mappings. In this paper we prove a generalization of the Product Formula when one factor is of the Identity+Compact type and the other is an A-compact mapping.

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A useful property of the Brouwer degree relates the degree of a composition of maps to the degree of each map. This property, which can be generalized for the Leray Schauder degree and in some cases for the A-proper maps [see 4], is called the Product Formula. \newline In [3] we develop a generalized degree theory for a class of mappings, this class contains the class of A-proper mappings and ... [Show full abstract] compact mappings, In this paper we prove a generalization of the Product Formula when one factor is of the Identity+Compact type and the other is an A-compact mapping.

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