Real Analysis Exchange

Algebraic Properties of Some Compact Spaces

F. Azarpanah

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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.%†\\

Article information

Real Anal. Exchange, Volume 25, Number 1 (1999), 317-328.

First available in Project Euclid: 5 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54C40: Algebraic properties of function spaces [See also 46J10]

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


Azarpanah, F. Algebraic Properties of Some Compact Spaces. Real Anal. Exchange 25 (1999), no. 1, 317--328.

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