# On the properties of the solution set map to Volterra integral inclusion

## TL;DR

This paper investigates the topological properties of the solution set for multivalued Volterra integral inclusions in Banach spaces, establishing its structure and continuity features without additional conditions.

## Contribution

It proves the solution set is an R_delta set, has a continuous single-valued selection, and that the solution set map's image of convex sets is acyclic, with solution sets being absolute retracts.

## Key findings

- Solution set is R_delta in Banach spaces.
- Solution set map has a continuous single-valued selection.
- Solution sets are absolute retracts.

## Abstract

For the multivalued Volterra integral equation defined in a Banach space, the set of solutions is proved to be $R_\delta$, without auxiliary conditions imposed in Theorem 6 [J. Math. Anal. Appl. 403 (2013), 643-666]. It is shown that the solution set map, corresponding to this Volterra integral equation, possesses a continuous singlevalued selection. The image of a convex set under solution set map is acyclic. The solution set to Volterra integral inclusion in a separable Banach space and the preimage of this set through the Volterra integral operator are shown to be absolute retracts.