JP Journal of Geometry and Topology
Volume 2, Issue 3, Pages 223 - 230
(November 2002)
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CLOSED INVERSE IMAGES OF RELATIVELY SUBPARACOMPACT SPACES
Ying Ge (P. R. China)
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Abstract:
In this paper, we prove that
perfect mappings inversely preserve k-subparacompactness
for k = 1, 2, 1*, without requiring the regularity of the spaces
involved. As an application of these results, we
answer a question on 2-paracompactness posed by
Qu and Yasui in [Scientiae Mathematicae
Japonicae 54 (2001), 281-287] affirmatively.
Also, we prove that closed Lindelöf mappings
inversely preserve the above k-subparacompactness
if the domains are regular, and give a
counterexample to show that the regularity of
the domains cannot be omitted. |
| Keywords and phrases: subparacompact, k-subparacompact (k = 1,
2, 1*), perfect mapping, Lindelöf mapping, regularity. |
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