A base property in paracompact products and its applications

For a paracompact space X, a base A of X is called an LF-base if every open cover of X has a locally finite open refinement by member of A. Let X and Y be paracompact spaces with LF-bases A and B, respectively. Assuming that the product X×Y is paracompact, we consider when A×B={A×B: A∈A and B∈B} is an LF-base of X×Y. Applying the argument here, we obtain several results for the strong rectangularity and the base-paracompactness of paracompact products.