Some spaces related to topological inequalities proven by the Erdős-Rado theorem

Author:
William G. Fleissner

Journal:
Proc. Amer. Math. Soc. **71** (1978), 313-320

MSC:
Primary 54A25; Secondary 02K05

DOI:
https://doi.org/10.1090/S0002-9939-1978-0493930-4

MathSciNet review:
0493930

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Abstract: The Erdös-Rado theorem is very useful in proving cardinal inequalities in topology. It has been suggested that certain of these inequalities might be strengthened. We note that trees constructed by Jensen and Gregory using various extra axioms of set theory yield several counterexamples to these suggestions; for example, a space , answering a question of Hajnal and Juhász. We consider the apparently similar relation between , and of Ginsburg and Woods. Using combinatorial consequences of , we construct tree families, and establish that, assuming , an infinite cardinal is weakly compact .

We consider products of countable chain condition spaces, and show that, using Cohen forcing that ( can be anything allowed by König's theorem and there are spaces ). A variation is a space *W* with the property .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0493930-4

Keywords:
Cardinal functions in topology,
trees,
,
Erdös-Rado theorem,
cellularity,
character,
spread,
diagonal,
products of ccc spaces,
Cohen forcing

Article copyright:
© Copyright 1978
American Mathematical Society