## Bulletin of the Belgian Mathematical Society - Simon Stevin

### A note on the lattices $DP(X)$ and $K(X)$

#### 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 $K(X)$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 2 (2013), 301-308.

Dates
First available in Project Euclid: 23 May 2013

https://projecteuclid.org/euclid.bbms/1369316546

Digital Object Identifier
doi:10.36045/bbms/1369316546

Mathematical Reviews number (MathSciNet)
MR3082766

Zentralblatt MATH identifier
1267.54015

#### Citation

Das, Tarun; Shah, Sejal. A note on the lattices $DP(X)$ and $K(X)$. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 2, 301--308. doi:10.36045/bbms/1369316546. https://projecteuclid.org/euclid.bbms/1369316546