Hereditarily $σ$-metacompact function spaces - Junnila, Heikki (Topology Proceedings, 2025)
Let $X$ be a compact space. We consider conditions on $X$ which ensure that the function space $C_p(X)$ is hereditarily $σ$-metacompact. The conditions involve $k$-networks with special properties. We prove that $C_p(X)$ is hereditarily $σ$-metacompact provided that either $X$ has a $σ$-pointwise-closure-preserving closed $k$-network or $X$ is supercompact.