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On closed inverse images of mesocompact spaces

Ge Y.

Fasciculi Mathematici

2005

Nr 36

27-32

In this paper, we prove that mesocompactness is inversely preserved under paracompact mappings with regular images. As an application of this result, we prove that mesocompactness is inversely preserved under closed Lindelof mappings with regular domains and images, which answers a question on mesocompactness posed by S. Lin. We also give a counterexample to show that the regularity of domains in this application can not be omitted.