On the embedding and developability of mapping spaces with compact open topology (Q2701860)

The paper investigates properties of \(C(X,Y)\), endowed with compact-open topology, inherited from \(X\) or \(Y\). NEWLINENEWLINENEWLINETheorem 2.3: If \(X\) is a compact metrizable space and \(Y\) has a \(G_\delta\)-diagonal then \(C(X,Y)\) is homeomorphic to a \(G_\delta\)-set in the hyperspace of compact subsets of \(X\times Y\) with Vietoris topology. NEWLINENEWLINENEWLINETheorem 3.1: If \(X\) is compact and \(Y\) has a (regular) \(G_\delta\)-diagonal then \(C(X,Y)\) has a (regular) \(G_\delta\)-diagonal. NEWLINENEWLINENEWLINETheorem 3.5: For a hemicompact \(X\), \(C(X,Y)\) is a Moore space having a regular \(G_\delta\)-diagonal iff \(Y\) has the same property.