Some cardinal function relationships between CP(X) and finite powers of a space X

AbstractNew bounds for the spread and hereditary density of the finite powers of the domain space X are obtained in terms of CP(X), the space of continuous real-valued functions with the topology of pointwise convergence. Sharp bounds are found for spaces X that include: spaces with a Gδ-diagonal, topological vector spaces, and Lindelöf homogeneous spaces. Corollaries of these will give bounds on the spread and hereditary Lindelöf degree of CP(X)2