On closed inverse images of base-paracompact spaces

In this paper, we prove that every base-paracompact mapping $f\colon X\longrightarrow Y$ inversely preserves base-paracompactness if $w(X)\ge w(Y)$, where $w(X)$ and $w(Y)$ denote the weight of $X$ and the weight of $Y$ respectively. As an application of this result, we prove that every closed Lindelöf mapping $f\colon X\longrightarrow Y$ inversely preserves base-paracompactness if $X$ is a regular space and $w(X)$ is a regular cardinality, where "$X$ is a regular space" cannot be relaxed to "$X$ is a Hausdorff space", which give some answers for a question on inverse images of base-paracompact spaces posed by L. Wu.