In this paper, we prove that every base-paracompact mapping f:X→ Y inversely preserves base-paracompactness if w(X) ≥ 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:X→ 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.
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