A note on hyperspaces and the compact-open topology

TL;DR

This paper investigates the continuity of the inclusion map from the space of continuous functions to the space of functions between hyperspaces of compact subsets, under the compact-open topology.

Contribution

It establishes the continuity of the inclusion map from map(X,Y) to map(K(X),K(Y)) in the context of hyperspaces and the compact-open topology.

Findings

The inclusion map is continuous under the compact-open topology.

Provides insights into the topology of hyperspaces and their function spaces.

Enhances understanding of the relationship between spaces of maps and hyperspaces.

Abstract

We prove that the inclusion of map(X,Y) into map(K(X),K(Y)) is continuous, where K(X) is the space of non-empty compact subsets of X (also known as the hyperspace of compact subsets of X), and both spaces of maps are endowed with the compact-open topology.