Geodesic
On closed inverse images of base-paracompact spaces
Lobachevskii journal of mathematics, Tome 21 (2006), pp. 57-63

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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.
Keywords: base-paracompactness, base-paracompact mapping, closed Lindelöf mapping, weight, regular cardinality. 
@article{LJM_2006_21_a3,
     author = {Y. Ge},
     title = {On closed inverse images of base-paracompact spaces},
     journal = {Lobachevskii journal of mathematics},
     pages = {57--63},
     publisher = {mathdoc},
     volume = {21},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_21_a3/}
}
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Y. Ge. On closed inverse images of base-paracompact spaces. Lobachevskii journal of mathematics, Tome 21 (2006), pp. 57-63. http://geodesic.mathdoc.fr/item/LJM_2006_21_a3/