The partially pre-ordered set of compactifications of \(C_p(X,Y)\) (Q2515759)

This paper examines the complete upper semilattice \(K\) of compactifications of \(C_p(X,Y)\) and shows that \(K\) is not a lattice if \(Y\) is first countable but not locally compact. If \(Y = \mathbb R\) (the space of real numbers), \(K\) is not a lattice if \(X\) is not pseudocompact or has a non-isolated point with countable character.