# On closed inverse images of base-paracompact spaces

## (*Lobachevskii Journal of Mathematics, Volume XXI*)

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.