The fixed point index for local condensing maps

We define below a fixed point index for local condensing maps f defined on open subset of «nice» metric ANR's. We prove that all the properties of classical fixed point index for continuous maps defined in compact polyhedra have appropriate generalizations. If our map is compact (a special case of a condensing map) and defined on an open subset of a Banach space, we prove that our fixed point index agrees with Leray-Schauder degree.