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Compactness of Powers of ω

Paolo Lipparini (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.

Kappa-Slender Modules

Radoslav Dimitric (2020)

Communications in Mathematics

For an arbitrary infinite cardinal κ , we define classes of κ -cslender and κ -tslender modules as well as related classes of κ -hmodules and initiate a study of these classes.

Locally compact linearly Lindelöf spaces

Kenneth Kunen (2002)

Commentationes Mathematicae Universitatis Carolinae

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.

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