Journal of the Mathematical Society of Japan

$\kappa$-Ohio completeness

Désirée BASILE, Guit-Jan RIDDERBOS, and Jan VAN MILL

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Abstract

Generalizing the Ohio completeness property, we introduce the notion of $\kappa$-Ohio completeness. Although many results from a previous paper by the authors may easily be adapted for this new property, there are also some interesting differences. We provide several examples to illustrate this. We also have a consistency result; depending on the value of the cardinal $\mathfrak{d}$, the countable union of open and $\omega_{1}$-Ohio complete subspaces may or may not be $\omega_{1}$-Ohio complete.

Article information

Source
J. Math. Soc. Japan Volume 61, Number 4 (2009), 1293-1301.

Dates
First available in Project Euclid: 6 November 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1257520508

Digital Object Identifier
doi:10.2969/jmsj/06141293

Mathematical Reviews number (MathSciNet)
MR2588512

Subjects
Primary: 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54G20: Counterexamples
Secondary: 54B05: Subspaces 54B25

Keywords
$\kappa$-Ohio complete sum theorems compactification

Citation

BASILE, Désirée; VAN MILL, Jan; RIDDERBOS, Guit-Jan. κ -Ohio completeness. Journal of the Mathematical Society of Japan 61 (2009), no. 4, 1293--1301. doi:10.2969/jmsj/06141293. http://projecteuclid.org/euclid.jmsj/1257520508.


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