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 $X-A$ from the lattice theoretic properties of $DP(X,A)$. Finally, we use them to obtain Thrivikraman's results concerning $\beta X-X$ and $K(X)$ and, Magill's result concerning the automorphism group of the lattice $K(X)$.
Citation
Tarun Das. Sejal Shah. "A note on the lattices $DP(X)$ and $K(X)$." Bull. Belg. Math. Soc. Simon Stevin 20 (2) 301 - 308, may 2013. https://doi.org/10.36045/bbms/1369316546
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