# An Extension of the Notion of Zero-Epi Maps to the Context of Topological Spaces

### Massimo Furi

Università di Firenze, Italy### A. Vignoli

Università di Roma 'Tor Vergata', Italy

## Abstract

We introduce the class of hyper-solvable equations whose concept may be regarded as an extension to the context of topological spaces of the known notion of 0-epi maps. After collecting some notation, definitions and preliminary results we give a homotopy principle for hyper-solvable equations. We provide examples showing how these equations arise in the framework of Leray-Schauder degree, Lefschetz number theory and essential compact vector fields in the sense of A. Granas.

## Cite this article

Massimo Furi, A. Vignoli, An Extension of the Notion of Zero-Epi Maps to the Context of Topological Spaces. Z. Anal. Anwend. 21 (2002), no. 2, pp. 485–493

DOI 10.4171/ZAA/1088