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A note on the lattice of density preserving maps

Published online by Cambridge University Press:  17 April 2009

Sejal Shah  and
T.K. Das
Sejal Shah
Affiliation:
Department of Mathematics, Faculty of Science, The M.S. University of Baroda, Vadodara - 390002, India, e-mail: [email protected], [email protected]
T.K. Das
Affiliation:
Department of Mathematics, Faculty of Science, The M.S. University of Baroda, Vadodara - 390002, India, e-mail: [email protected], [email protected]
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 2005

References

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