Journal of the Mathematical Society of Japan

Topological extensions with compact remainder


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Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial order $\leq$) and the topology of certain subspaces of the outgrowth $\beta X\setminus X$. The cases when $\mathfrak{P}$ is either pseudocompactness or realcompactness are studied in more detail.

Article information

J. Math. Soc. Japan, Volume 67, Number 1 (2015), 1-42.

First available in Project Euclid: 22 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D60: Realcompactness and realcompactification
Secondary: 54D40: Remainders

Stone–Čech compactification Hewitt realcompactification pseudocompactification realcompactification Mrówka's condition (W) compactness-like topological property


KOUSHESH, M. R. Topological extensions with compact remainder. J. Math. Soc. Japan 67 (2015), no. 1, 1--42. doi:10.2969/jmsj/06710001.

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