Real Analysis Exchange

Algebraic Properties of Some Compact Spaces

F. Azarpanah

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Abstract

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

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

Dates
First available in Project Euclid: 5 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1231187606

Mathematical Reviews number (MathSciNet)
MR1758008

Zentralblatt MATH identifier
1015.54008

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

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

Citation

Azarpanah, F. Algebraic Properties of Some Compact Spaces. Real Anal. Exchange 25 (1999), no. 1, 317--328. https://projecteuclid.org/euclid.rae/1231187606


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References

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