Open Access
1999/2000 Algebraic Properties of Some Compact Spaces
F. Azarpanah
Real Anal. Exchange 25(1): 317-328 (1999/2000).


Almost discrete spaces and in particular, the one-point compactifications of discrete spaces are algebraically characterized. This algebraic characterization is then used to show that whenever $C(X)\approx C(Y)$ and $X$ is the one-point compactification of a discrete space, then $Y$ is too. Some equivalent algebraic properties of almost locally compact spaces and nowhere compact spaces are studied. Using these properties we show that every completely regular space can be decomposed into two disjoint subspaces, where one is an open almost locally compact space and the other is a nowhere compact space. Finally, we will show that $X$ is Lindel\"{o}f if and only if every strongly divisible ideal in $C(X)$ is fixed.%†\\


Download Citation

F. Azarpanah. "Algebraic Properties of Some Compact Spaces." Real Anal. Exchange 25 (1) 317 - 328, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.54008
MathSciNet: MR1758008

Primary: 54C40

Keywords: almost locally compact , essential ideal , Lindel\"{o}f and almost discrete space , nowhere compact , strongly divisible ideal

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
Back to Top