A note on the lattice of density preserving maps
2005 ◽
Vol 72
(1)
◽
pp. 1-6
Keyword(s):
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.
1974 ◽
Vol 53
◽
pp. 127-135
◽
1994 ◽
Vol 50
(3)
◽
pp. 445-449
◽
1986 ◽
Vol 41
(1)
◽
pp. 115-137
◽
1972 ◽
Vol 2
(4)
◽
pp. 287-291
◽
Keyword(s):
1974 ◽
Vol 26
(1)
◽
pp. 42-49
◽
1992 ◽
Vol 35
(2)
◽
pp. 271-283
◽
2019 ◽
Vol 2019
◽
pp. 1-7