# On closed inverse images of base-paracompact spaces

## (Lobachevskii Journal of Mathematics, Vol.21, pp.57-63 )

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.