Bull. Austral. Math. Soc. 72(1) pp.1--6, 2005.
A note on the lattice of density preserving maps
Sejal Shah |
T.K. Das |
.
Abstract
We study here the poset DP(X) of density preserving continuous
maps defined on a Hausdorff sapce X and show that it is a complete lattice for a
compact Hausdorff space without isolated points. We further show
that for countably compact T3 spaces X and Y
without isolated points, DP(X) and DP(Y) are order isomorphic if and only
if X and Y are homeomorphic. Finally, Magill's result
on the remainder of a locally compact Hausdorff space is deduced
from the relation of DP(X)
with posets IP(X) of
covering maps and EK
(X) of compactifications respectively.
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[an error occurred while processing this directive]| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2162288 | Z'blatt-MATH: 02212180 |
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