Essential and inessential maps and continuation theorems (Q1975288)

In the present paper the notion of essential map [\textit{A. Granas}, C. R. Acad. Sci. Paris, Sér. A 282, 983-985 (1976; Zbl 0348.47039)] is extended to a larger class of maps. For this new notion it is proved that if \(0\) is essential and \(0\cong F\), then \(F\) is essential. A discussion of inessential maps is also included in the paper as well as a generalization of Krasnoselskii's compression and expansion theorem.