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- Title
A note on the lattices DP(X) and K(X).
- Authors
Das, Tarun; Shah, Sejal
- Abstract
Using the order structure of the lattice DP(X) of density preserving continuous maps on a Hausdorff space X without isolated points, we describe closed nowhere dense subsets of X and, for a subspace A of X, we also deduce topological properties of the space X- A fromthe lattice theoretic properties of DP(X, A). Finally, we use them to obtain Thrivikraman's results concerning βX - X and K(X) and, Magill's result concerning the automorphism group of the lattice K(X).
- Subjects
LATTICE theory; DENSITY; CONTINUOUS functions; AUTOMORPHISMS; COMPACTIFICATION (Mathematics); HAUSDORFF spaces
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013, Vol 20, Issue 2, p301
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/bbms/1369316546